Finite Group Databasebeta

← Group #13167088

Character table — Group #13167088

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444444444444444488888888888888889999121212121212121212121212181818181818242424242424242424242424363636363636545454545454545472727272
order1222344666333366666666666612123666121212121212121212121212222244441212121212121212446666121212121212121212121212444412128888888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ511111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1
χ611111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ711111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ811111-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-111
χ91-11-111-1-11-11111-1-1-1-11111-1-1-1-11-11-1-111111-1-1-1-111-1-111-1-1i−ii−iii−i−iii−i−i-1111-1-1iii−i−i−iiii−i−i−ii−ii−i1-111-1-111-1-1i−ii−i
χ101-11-111-1-11-11111-1-1-1-11111-1-1-1-11-11-1-111111-1-1-1-111-1-111-1-1i−ii−iii−i−iii−i−i-1111-1-1iii−i−i−iiii−i−i−i−ii−ii1-1-1-111-1-111−ii−ii
χ111-11-111-1-11-11111-1-1-1-11111-1-1-1-11-11-1-111111-1-1-1-111-1-111-1-1−ii−ii−i−iii−i−iii-1111-1-1−i−i−iiii−i−i−iiiii−ii−i1-1-1-111-1-111i−ii−i
χ121-11-111-1-11-11111-1-1-1-11111-1-1-1-11-11-1-111111-1-1-1-111-1-111-1-1−ii−ii−i−iii−i−iii-1111-1-1−i−i−iiii−i−i−iiii−ii−ii1-111-1-111-1-1−ii−ii
χ131-11-11-11-11-11111-1-1-1-11111-1-1-1-1-111-1-11-1-1-1-11111-1-111-1-111i−i−iiii−i−i−i−iii-11-1-111iii−i−i−i−i−i−iiiii−i−ii1-111-1-1-1-111i−i−ii
χ141-11-11-11-11-11111-1-1-1-11111-1-1-1-1-111-1-11-1-1-1-11111-1-111-1-111i−i−iiii−i−i−i−iii-11-1-111iii−i−i−i−i−i−iiii−iii−i1-1-1-11111-1-1−iii−i
χ151-11-11-11-11-11111-1-1-1-11111-1-1-1-1-111-1-11-1-1-1-11111-1-111-1-111−iii−i−i−iiiii−i−i-11-1-111−i−i−iiiiiii−i−i−ii−i−ii1-1-1-11111-1-1i−i−ii
χ161-11-11-11-11-11111-1-1-1-11111-1-1-1-1-111-1-11-1-1-1-11111-1-111-1-111−iii−i−i−iiiii−i−i-11-1-111−i−i−iiiiiii−i−i−i−iii−i1-111-1-1-1-111−iii−i
χ1722222222222222222222222222222222222222222222-2-2-2-2000000000000-2-2-2-2-2-20000000000000000-2-2000000000000
χ1822222-2-22222222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000-2-222220000000000000000-2-2000000000000
χ192222-122-1-1-122-1-122-1-122-1-12-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-12-1-12-1-12-1-12-1-10000-1-1000000000000
χ202222-122-1-1-122-1-122-1-122-1-12-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-12222-2-2-2-21111111122-1-1-1-1-211-211-211-2110000-1-1000000000000
χ212222-122-1-1-122-1-122-1-122-1-12-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-1-2-2-2-20000−i3i3−i3i3−i3i3−i3i3-2-211110−i3i30−i3i30−i3i30−i3i3000011000000000000
χ222222-122-1-1-122-1-122-1-122-1-12-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-1-2-2-2-20000i3−i3i3−i3i3−i3i3−i3-2-211110i3−i30i3−i30i3−i30i3−i3000011000000000000
χ232222-1-2-2-1-1-122-1-122-1-122-1-12-1-1211-1-1-1-1-2-211-2-211111122220000−i3i3−i3i3i3−i3i3−i3-2-2-1-1-1-10−i3i30−i3i30i3−i30i3−i3000011000000000000
χ242222-1-2-2-1-1-122-1-122-1-122-1-12-1-1211-1-1-1-1-2-211-2-211111122220000i3−i3i3−i3−i3i3−i3i3-2-2-1-1-1-10i3−i30i3−i30−i3i30−i3i3000011000000000000
χ252222-1-2-2-1-1-122-1-122-1-122-1-12-1-1211-1-1-1-1-2-211-2-2111111-2-2-2-222-2-2-1-1-1-111112211112-1-12-1-1-211-2110000-1-1000000000000
χ262222-1-2-2-1-1-122-1-122-1-122-1-12-1-1211-1-1-1-1-2-211-2-2111111-2-2-2-2-2-2221111-1-1-1-1221111-211-2112-1-12-1-10000-1-1000000000000
χ2722-2-22002-2-222222222-2-2-2-2-2-2-2-20022-2-20000000000002-22-2000000000000002-22-20000000000000000002−22−22−22−20000
χ2822-2-22002-2-222222222-2-2-2-2-2-2-2-20022-2-20000000000002-22-2000000000000002-22-2000000000000000000−22−22−22−220000
χ2922-2-22002-2-222222222-2-2-2-2-2-2-2-20022-2-2000000000000-22-2200000000000000-22-220000000000000000002−22−2−22−220000
χ3022-2-22002-2-222222222-2-2-2-2-2-2-2-20022-2-2000000000000-22-2200000000000000-22-22000000000000000000−22−222−22−20000
χ312-22-222-2-22-22222-2-2-2-22222-2-2-2-22-22-2-222222-2-2-2-222-2-2-2-2220000000000002-2-2-2220000000000000000-22000000000000
χ322-22-22-22-22-22222-2-2-2-22222-2-2-2-2-222-2-22-2-2-2-22222-2-22222-2-20000000000002-222-2-20000000000000000-22000000000000
χ332-22-2-12-21-1122-1-1-2-21122-1-1-211-2-11-111-122-1-1-2-211-1-11122-2-22i−2i2i−2i−i−iii−i−iii-22-1-1112i−i−i−2iii2i−i−i−2iii0000-11000000000000
χ342-22-2-12-21-1122-1-1-2-21122-1-1-211-2-11-111-122-1-1-2-211-1-11122-2-2−2i2i−2i2iii−i−iii−i−i-22-1-111−2iii2i−i−i−2iii2i−i−i0000-11000000000000
χ352-22-2-12-21-1122-1-1-2-21122-1-1-211-2-11-111-122-1-1-2-211-1-111-2-22200003−3−333−3−332-211-1-103−30−3303−30−3300001-1000000000000
χ362-22-2-12-21-1122-1-1-2-21122-1-1-211-2-11-111-122-1-1-2-211-1-111-2-2220000−333−3−333−32-211-1-10−3303−30−3303−300001-1000000000000
χ372-22-2-1-221-1122-1-1-2-21122-1-1-211-21-1-111-1-2-21122-1-111-1-122-2-200003−3−33−333−32-2-1-11103−30−330−3303−300001-1000000000000
χ382-22-2-1-221-1122-1-1-2-21122-1-1-211-21-1-111-1-2-21122-1-111-1-122-2-20000−333−33−3−332-2-1-1110−3303−303−30−3300001-1000000000000
χ392-22-2-1-221-1122-1-1-2-21122-1-1-211-21-1-111-1-2-21122-1-111-1-1-2-2222i−2i−2i2i−i−iiiii−i−i-2211-1-12i−i−i−2iii−2iii2i−i−i0000-11000000000000
χ402-22-2-1-221-1122-1-1-2-21122-1-1-211-21-1-111-1-2-21122-1-111-1-1-2-222−2i2i2i−2iii−i−i−i−iii-2211-1-1−2iii2i−i−i2i−i−i−2iii0000-11000000000000
χ412-2-22200-2-222222-2-2-2-2-2-2-2-22222002-22-20000000000002-2-22000000000000002-2-220000000000000000002−2−222−2−220000
χ422-2-22200-2-222222-2-2-2-2-2-2-2-22222002-22-20000000000002-2-22000000000000002-2-22000000000000000000−222−2−222−20000
χ432-2-22200-2-222222-2-2-2-2-2-2-2-22222002-22-2000000000000-222-200000000000000-222-20000000000000000002−2−22−222−20000
χ442-2-22200-2-222222-2-2-2-2-2-2-2-22222002-22-2000000000000-222-200000000000000-222-2000000000000000000−222−22−2−220000
χ4544444444441-2111-2111-211111-244-2-2-2-21-2111-211-2-2-2-20000222222222222000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ4644444444441-2111-2111-211111-244-2-2-2-21-2111-211-2-2-2-20000-2-2-2-2-2-2-2-2-2-2-2-2000000111111111111000000000000000000
χ474444444444-21-2-2-21-2-2-21-2-2-2-2-21441111-21-2-2-21-2-21111000000000000000000000000000000000022220000000000-1-1-1-1
χ484444444444-21-2-2-21-2-2-21-2-2-2-2-21441111-21-2-2-21-2-211110000000000000000000000000000000000-2-2-2-200000000001111
χ4944444-4-44441-2111-2111-211111-2-4-4-2-2-2-2-12-1-1-12-1-12222000022-2-22222-2-2-2-2000000-1-1-1-1-1-1111111000000000000000000
χ5044444-4-44441-2111-2111-211111-2-4-4-2-2-2-2-12-1-1-12-1-122220000-2-222-2-2-2-22222000000111111-1-1-1-1-1-1000000000000000000
χ5144444-4-4444-21-2-2-21-2-2-21-2-2-2-2-21-4-411112-1222-122-1-1-1-1000000000000000000000000000000000022-2-20000000000-1-111
χ5244444-4-4444-21-2-2-21-2-2-21-2-2-2-2-21-4-411112-1222-122-1-1-1-10000000000000000000000000000000000-2-222000000000011-1-1
χ534444-244-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2-2-211111-2−1−3i32−1+3i321-2−1−3i32−1+3i32111100002222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32000000000000000000
χ544444-244-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2-2-211111-2−1−3i32−1+3i321-2−1−3i32−1+3i3211110000-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i30000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ554444-244-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2-2-211111-2−1+3i32−1−3i321-2−1+3i32−1−3i32111100002222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32000000000000000000
χ564444-244-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2-2-211111-2−1+3i32−1−3i321-2−1+3i32−1−3i3211110000-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i30000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ574444-2-4-4-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2221111-121+3i321−3i32-121+3i321−3i32-1-1-1-1000022-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3000000-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ584444-2-4-4-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2221111-121+3i321−3i32-121+3i321−3i32-1-1-1-10000-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i30000001−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i32000000000000000000
χ594444-2-4-4-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2221111-121−3i321+3i32-121−3i321+3i32-1-1-1-1000022-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3000000-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ604444-2-4-4-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2221111-121−3i321+3i32-121−3i321+3i32-1-1-1-10000-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i30000001−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i32000000000000000000
χ6144-4-4-200-22244-2-244-2-2-4-422-422-400-2-2220000000000004-44-400000000000000-22-22000000000000000000000000000000
χ6244-4-4-200-22244-2-244-2-2-4-422-422-400-2-222000000000000-44-44000000000000002-22-2000000000000000000000000000000
χ634-44-444-4-44-41-211-12-1-11-211-1-1-124-4-222-21-211-12-1-1-2-22200002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i000000−i−i−iiii−i−i−iiii000000000000000000
χ644-44-444-4-44-41-211-12-1-11-211-1-1-124-4-222-21-211-12-1-1-2-2220000−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i000000iii−i−i−iiii−i−i−i000000000000000000
χ654-44-444-4-44-4-21-2-22-122-21-2-2222-14-41-1-11-21-2-22-12211-1-100000000000000000000000000000000002i−2i2i−2i0000000000−ii−ii
χ664-44-444-4-44-4-21-2-22-122-21-2-2222-14-41-1-11-21-2-22-12211-1-10000000000000000000000000000000000−2i2i−2i2i0000000000i−ii−i
χ674-44-44-44-44-41-211-12-1-11-211-1-1-12-44-222-2-12-1-11-21122-2-200002i−2i−2i2i2i2i−2i−2i−2i−2i2i2i000000−i−i−iiiiiii−i−i−i000000000000000000
χ684-44-44-44-44-41-211-12-1-11-211-1-1-12-44-222-2-12-1-11-21122-2-20000−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i000000iii−i−i−i−i−i−iiii000000000000000000
χ694-44-44-44-44-4-21-2-22-122-21-2-2222-1-441-1-112-122-21-2-2-1-11100000000000000000000000000000000002i−2i−2i2i0000000000−iii−i
χ704-44-44-44-44-4-21-2-22-122-21-2-2222-1-441-1-112-122-21-2-2-1-1110000000000000000000000000000000000−2i2i2i−2i0000000000i−i−ii
χ714-44-4-24-42-221-2−1−3i32−1+3i32-121+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i322-221-1-111-2−1−3i32−1+3i32-121+3i321−3i3211-1-100002i−2i2i−2i2ζ222ζ14−2ζ22−2ζ142ζ222ζ14−2ζ22−2ζ14000000−i−ζ22−ζ14iζ22ζ14−i−ζ22−ζ14iζ22ζ14000000000000000000
χ724-44-4-24-42-221-2−1−3i32−1+3i32-121+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i322-221-1-111-2−1−3i32−1+3i32-121+3i321−3i3211-1-10000−2i2i−2i2i−2ζ22−2ζ142ζ222ζ14−2ζ22−2ζ142ζ222ζ14000000iζ22ζ14−i−ζ22−ζ14iζ22ζ14−i−ζ22−ζ14000000000000000000
χ734-44-4-24-42-221-2−1+3i32−1−3i32-121−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i322-221-1-111-2−1+3i32−1−3i32-121−3i321+3i3211-1-100002i−2i2i−2i2ζ142ζ22−2ζ14−2ζ222ζ142ζ22−2ζ14−2ζ22000000−i−ζ14−ζ22iζ14ζ22−i−ζ14−ζ22iζ14ζ22000000000000000000
χ744-44-4-24-42-221-2−1+3i32−1−3i32-121−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i322-221-1-111-2−1+3i32−1−3i32-121−3i321+3i3211-1-10000−2i2i−2i2i−2ζ14−2ζ222ζ142ζ22−2ζ14−2ζ222ζ142ζ22000000iζ14ζ22−i−ζ14−ζ22iζ14ζ22−i−ζ14−ζ22000000000000000000
χ754-44-4-2-442-221-2−1−3i32−1+3i32-121+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i3222-21-1-11-121+3i321−3i321-2−1−3i32−1+3i32-1-11100002i−2i−2i2i2ζ222ζ14−2ζ22−2ζ14−2ζ22−2ζ142ζ222ζ14000000−i−ζ22−ζ14iζ22ζ14iζ22ζ14−i−ζ22−ζ14000000000000000000
χ764-44-4-2-442-221-2−1−3i32−1+3i32-121+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i3222-21-1-11-121+3i321−3i321-2−1−3i32−1+3i32-1-1110000−2i2i2i−2i−2ζ22−2ζ142ζ222ζ142ζ222ζ14−2ζ22−2ζ14000000iζ22ζ14−i−ζ22−ζ14−i−ζ22−ζ14iζ22ζ14000000000000000000
χ774-44-4-2-442-221-2−1+3i32−1−3i32-121−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i3222-21-1-11-121−3i321+3i321-2−1+3i32−1−3i32-1-11100002i−2i−2i2i2ζ142ζ22−2ζ14−2ζ22−2ζ14−2ζ222ζ142ζ22000000−i−ζ14−ζ22iζ14ζ22iζ14ζ22−i−ζ14−ζ22000000000000000000
χ784-44-4-2-442-221-2−1+3i32−1−3i32-121−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i3222-21-1-11-121−3i321+3i321-2−1+3i32−1−3i32-1-1110000−2i2i2i−2i−2ζ14−2ζ222ζ142ζ222ζ142ζ22−2ζ14−2ζ22000000iζ14ζ22−i−ζ14−ζ22−i−ζ14−ζ22iζ14ζ22000000000000000000
χ794-4-44-20022-244-2-2-4-422-4-4224-2-2400-22-220000000000004-4-4400000000000000-222-2000000000000000000000000000000
χ804-4-44-20022-244-2-2-4-422-4-4224-2-2400-22-22000000000000-444-4000000000000002-2-22000000000000000000000000000000
χ818888-488-4-4-4-4222-4222-4222-4222-4-4-1-1-1-1-4222-4222-1-1-1-10000000000000000000000000000000000000000000000000000
χ828888-4-8-8-4-4-4-4222-4222-4222-422244-1-1-1-14-2-2-24-2-2-211110000000000000000000000000000000000000000000000000000
χ8388-8-88008-8-82-4222-422-24-2-2-2-2-2400-4-4440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-88008-8-8-42-4-4-42-4-44-244444-20022-2-20000000000000000000000000000000000000000000000000000000000000000
χ8588-8-8-400-4442-4−1−3i3−1+3i32-4−1−3i3−1+3i3-241+3i31−3i3-21+3i31−3i340022-2-20000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8-400-4442-4−1+3i3−1−3i32-4−1+3i3−1−3i3-241−3i31+3i3-21−3i31+3i340022-2-20000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-400-444-4222-42224-2-2-24-2-2-200-1-1110000000033−3333−330000000000000000000000000000000000000000000000000000
χ8888-8-8-400-444-4222-42224-2-2-24-2-2-200-1-11100000000−3333−33330000000000000000000000000000000000000000000000000000
χ898-88-8-48-84-44-42224-2-2-2-42224-2-2-2-44-111-1-42224-2-2-2-1-1110000000000000000000000000000000000000000000000000000
χ908-88-8-4-884-44-42224-2-2-2-42224-2-2-24-4-111-14-2-2-2-422211-1-10000000000000000000000000000000000000000000000000000
χ918-8-88800-8-882-422-24-2-2-24-2-2222-400-44-440000000000000000000000000000000000000000000000000000000000000000
χ928-8-88800-8-88-42-4-44-2444-244-4-4-42002-22-20000000000000000000000000000000000000000000000000000000000000000
χ938-8-88-40044-42-4−1−3i3−1+3i3-241+3i31−3i3-241+3i31−3i32−1−3i3−1+3i3-4002-22-20000000000000000000000000000000000000000000000000000000000000000
χ948-8-88-40044-42-4−1+3i3−1−3i3-241−3i31+3i3-241−3i31+3i32−1+3i3−1−3i3-4002-22-20000000000000000000000000000000000000000000000000000000000000000
χ958-8-88-40044-4-42224-2-2-24-2-2-2-422200-11-110000000033−33−33330000000000000000000000000000000000000000000000000000
χ968-8-88-40044-4-42224-2-2-24-2-2-2-422200-11-1100000000−333333−330000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.