Finite Group Databasebeta

← Group #13167053

Character table — Group #13167053

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222224444444444444444444444888888888888889999121212121212121212121212181818181818181818181818181824242424242424242424242436363636363636363636108108108108
order12442346121233336666666121212121212121212121236666661212121212121222442244666612121212244444444466121266666612121212121261212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ51111-11-11111111-11111-1-1-111-1-11111111-1-1-1-1-11-1-1-111-1-1-1-1-1-11-11-111-1-111-1-111iiii−i−i−i−i-1-1-1-1111-1-1-1111-1-1-111iiii−i−i−i−iii−i−i
χ61111-11-11111111-11111-1-1-111-1-11111111-1-1-1-1-11-1-1-111-1-1-1-1-1-11-11-111-1-111-1-111−i−i−i−iiiii-1-1-1-1111-1-1-1111-1-1-111−i−i−i−iiiii−i−iii
χ71111-11-11111111-11111-1-1-111-1-11111111-1-1-1-1-11-1-1-111-1-1-1-1-1-1-11-11-1-111-1-11111iiii−i−i−i−i-1-1-1-1-1-1-1111-1-1-111111iiii−i−i−i−i−i−iii
χ81111-11-11111111-11111-1-1-111-1-11111111-1-1-1-1-11-1-1-111-1-1-1-1-1-1-11-11-1-111-1-11111−i−i−i−iiiii-1-1-1-1-1-1-1111-1-1-111111−i−i−i−iiiiiii−i−i
χ911-1-111-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-111-1111-1-111-1-1-1-111111-1-1-1-1-1-1111-1111-1-111-1-11-11-1
χ1011-1-111-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-111-11-1-111-1-111-1-111111-1-1-1-1-1-1111-11-1-111-1-111-11-11
χ1111-1-111-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-111-111-1-1-11111-1-1-1111-1-111-1-1-1-111-1-1-1111111-1-1-1-1111-1-111-1-1-11-11
χ1211-1-111-11-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-111-111-1-1-11111-1-1-11-1-111-1-111-1-111-1-1-1111111-1-1-1-11-1-111-1-1111-11-1
χ1311-1-1-1111-1-11111-11111-1-11-1-111-1-1-1-1-1-11-1-1-1-1-11111-1-11111-1-111-1-11111-1-1-1-1-11ii−i−i−i−iii11-1-1111111-1-1-1-1-1-1-11ii−i−i−i−iiii−i−ii
χ1411-1-1-1111-1-11111-11111-1-11-1-111-1-1-1-1-1-11-1-1-1-1-11111-1-11111-1-111-1-11111-1-1-1-1-11−i−iiiii−i−i11-1-1111111-1-1-1-1-1-1-11−i−iiiii−i−i−iii−i
χ1511-1-1-1111-1-11111-11111-1-11-1-111-1-1-1-1-1-11-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-11ii−i−i−i−iii11-1-1-1-1-1-1-1-1111111-11ii−i−i−i−iii−iii−i
χ1611-1-1-1111-1-11111-11111-1-11-1-111-1-1-1-1-1-11-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-11−i−iiiii−i−i11-1-1-1-1-1-1-1-1111111-11−i−iiiii−i−ii−i−ii
χ172222222222222222222222222222222222222222222222-2-2-2-2000000000000-2-200000000-2-2-2-2000000000000-2-2000000000000
χ1822222-12-1-1-122-1-1-122-1-122-1222222-1-1-1-1-12-1-1-1-1-12-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12200000000-1-1-1-12-1-12-1-12-1-12-1-1-1-1000000000000
χ1922222-12-1-1-122-1-1-122-1-122-1222222-1-1-1-1-12-1-1-1-1-12-1-1-1-1-1-12222-2-2-2-2111111112200000000-1-1-1-1-211-211-211-211-1-1000000000000
χ2022222-12-1-1-122-1-1-122-1-122-1222222-1-1-1-1-12-1-1-1-1-12-1-1-1-1-1-1-2-2-2-20000−i3i3−i3i3−i3i3−i3i3-2-20000000011110−i3i30−i3i30−i3i30−i3i311000000000000
χ2122222-12-1-1-122-1-1-122-1-122-1222222-1-1-1-1-12-1-1-1-1-12-1-1-1-1-1-1-2-2-2-20000i3−i3i3−i3i3−i3i3−i3-2-20000000011110i3−i30i3−i30i3−i30i3−i311000000000000
χ222222-22-22222222-22222-2-2-222-2-22222222-2-2-2-2-22-2-2-222-2-22222000000000000-2-2000000002222000000000000-2-2000000000000
χ232222-2-1-2-1-1-122-1-1122-1-1-2-2122-2-222-1-1-1-1-1-21111-1-211-1-11122220000−i3i3i3−i3−i3i3i3−i3-2-200000000-1-1-1-10−i3i30i3−i30−i3i30i3−i311000000000000
χ242222-2-1-2-1-1-122-1-1122-1-1-2-2122-2-222-1-1-1-1-1-21111-1-211-1-11122220000i3−i3−i3i3i3−i3−i3i3-2-200000000-1-1-1-10i3−i30−i3i30i3−i30−i3i311000000000000
χ252222-2-1-2-1-1-122-1-1122-1-1-2-2122-2-222-1-1-1-1-1-21111-1-211-1-111-2-2-2-22-22-2-1-111-1-111220000000011112-1-1-2112-1-1-211-1-1000000000000
χ262222-2-1-2-1-1-122-1-1122-1-1-2-2122-2-222-1-1-1-1-1-21111-1-211-1-111-2-2-2-2-22-2211-1-111-1-122000000001111-2112-1-1-2112-1-1-1-1000000000000
χ2722-2-222-22-2-222222222222-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-222-2-20000000000002-20000000022-2-20000000000002-2000000000000
χ2822-2-22-1-2-11122-1-1-122-1-1221-2-2-2-2-2-21111-12-1-1-1-1-1-211111122-2-20000−i3i3i3−i3i3−i3−i3i32-200000000-1-1110−i3i30i3−i30i3−i30−i3i3-11000000000000
χ2922-2-22-1-2-11122-1-1-122-1-1221-2-2-2-2-2-21111-12-1-1-1-1-1-211111122-2-20000i3−i3−i3i3−i3i3i3−i32-200000000-1-1110i3−i30−i3i30−i3i30i3−i3-11000000000000
χ3022-2-22-1-2-11122-1-1-122-1-1221-2-2-2-2-2-21111-12-1-1-1-1-1-2111111-2-2222-2-22-1-11111-1-1-220000000011-1-12-1-1-211-2112-1-11-1000000000000
χ3122-2-22-1-2-11122-1-1-122-1-1221-2-2-2-2-2-21111-12-1-1-1-1-1-2111111-2-222-222-211-1-1-1-111-220000000011-1-1-2112-1-12-1-1-2111-1000000000000
χ3222-2-2-2222-2-22222-22222-2-22-2-222-2-2-2-2-2-22-2-2-2-2-22222-2-222-2-2220000000000002-200000000-2-2220000000000002-2000000000000
χ3322-2-2-2-12-11122-1-1122-1-1-2-2-1-2-222-2-21111-1-21111-12-1-111-1-122-2-222-2-2-1-1-1-11111-2200000000-1-1112-1-12-1-1-211-2111-1000000000000
χ3422-2-2-2-12-11122-1-1122-1-1-2-2-1-2-222-2-21111-1-21111-12-1-111-1-122-2-2-2-2221111-1-1-1-1-2200000000-1-111-211-2112-1-12-1-11-1000000000000
χ3522-2-2-2-12-11122-1-1122-1-1-2-2-1-2-222-2-21111-1-21111-12-1-111-1-1-2-2220000−i3i3−i3i3i3−i3i3−i32-20000000011-1-10−i3i30−i3i30i3−i30i3−i3-11000000000000
χ3622-2-2-2-12-11122-1-1122-1-1-2-2-1-2-222-2-21111-1-21111-12-1-111-1-1-2-2220000i3−i3i3−i3−i3i3−i3i32-20000000011-1-10i3−i30i3−i30−i3i30−i3i3-11000000000000
χ372-22i−2i020-22i−2i22220-2-2-2-20002i−2i002i−2i2i2i−2i−2i200000-20002i−2i002-22i−2i000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i2-22i−2i000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ382-22i−2i020-22i−2i22220-2-2-2-20002i−2i002i−2i2i2i−2i−2i200000-20002i−2i002-22i−2i00000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i2-22i−2i00000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ392-22i−2i020-22i−2i22220-2-2-2-20002i−2i002i−2i2i2i−2i−2i200000-20002i−2i00-22−2i2i000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i-22−2i2i000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ402-22i−2i020-22i−2i22220-2-2-2-20002i−2i002i−2i2i2i−2i−2i200000-20002i−2i00-22−2i2i00000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i-22−2i2i00000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ412-2−2i2i020-2−2i2i22220-2-2-2-2000−2i2i00−2i2i−2i−2i2i2i200000-2000−2i2i002-2−2i2i000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i2-2−2i2i000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ422-2−2i2i020-2−2i2i22220-2-2-2-2000−2i2i00−2i2i−2i−2i2i2i200000-2000−2i2i002-2−2i2i00000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i2-2−2i2i00000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ432-2−2i2i020-2−2i2i22220-2-2-2-2000−2i2i00−2i2i−2i−2i2i2i200000-2000−2i2i00-222i−2i000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i-222i−2i000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ442-2−2i2i020-2−2i2i22220-2-2-2-2000−2i2i00−2i2i−2i−2i2i2i200000-2000−2i2i00-222i−2i00000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i-222i−2i00000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ4544444444441-2-2-241-2-2-21141111-2-2-2-2-2-21-2-2-2111-2-2-2111100000000000000000022222222000000000000000000-1-1-1-1-1-1-1-10000
χ4644444444441-2-2-241-2-2-21141111-2-2-2-2-2-21-2-2-2111-2-2-21111000000000000000000-2-2-2-2-2-2-2-2000000000000000000111111110000
χ474444444444-21114-2111-2-24-2-2-2-2111111-2111-2-2-2111-2-2-2-2000022222222222200000000000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ484444444444-21114-2111-2-24-2-2-2-2111111-2111-2-2-2111-2-2-2-20000-2-2-2-2-2-2-2-2-2-2-2-20000000000000011111111111100000000000000
χ4944444-24-2-2-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-2-2-2-2-2-211−1−3i32−1+3i32−1−3i32−1+3i3211−1−3i32−1+3i321111−1−3i32−1+3i32111100002222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i300000000000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i3200000000000000
χ5044444-24-2-2-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-2-2-2-2-2-211−1−3i32−1+3i32−1−3i32−1+3i3211−1−3i32−1+3i321111−1−3i32−1+3i3211110000-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i3000000000000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3200000000000000
χ5144444-24-2-2-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-2-2-2-2-2-211−1+3i32−1−3i32−1+3i32−1−3i3211−1+3i32−1−3i321111−1+3i32−1−3i32111100002222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i300000000000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i3200000000000000
χ5244444-24-2-2-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-2-2-2-2-2-211−1+3i32−1−3i32−1+3i32−1−3i3211−1+3i32−1−3i321111−1+3i32−1−3i3211110000-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i3000000000000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3200000000000000
χ534444-44-44441-2-2-2-41-2-2-2-1-1-411-1-1-2-2-2-2-2-21222-1-1122211-1-10000000000000000002i2i2i2i−2i−2i−2i−2i000000000000000000−i−i−i−iiiii0000
χ544444-44-44441-2-2-2-41-2-2-2-1-1-411-1-1-2-2-2-2-2-21222-1-1122211-1-1000000000000000000−2i−2i−2i−2i2i2i2i2i000000000000000000iiii−i−i−i−i0000
χ554444-44-4444-2111-4-211122-4-2-222111111-2-1-1-122-2-1-1-1-2-22200002-22-222-2-222-2-200000000000000-1-1-1111-1-1-111100000000000000
χ564444-44-4444-2111-4-211122-4-2-222111111-2-1-1-122-2-1-1-1-2-2220000-22-22-2-222-2-22200000000000000111-1-1-1111-1-1-100000000000000
χ574444-4-2-4-2-2-2-21−1−3i32−1+3i322-21−1−3i32−1+3i32222-2-22211−1−3i32−1+3i32−1−3i32−1+3i321-11+3i321−3i32-1-11-11+3i321−3i3211-1-100002-22-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i300000000000000-11+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i3200000000000000
χ584444-4-2-4-2-2-2-21−1−3i32−1+3i322-21−1−3i32−1+3i32222-2-22211−1−3i32−1+3i32−1−3i32−1+3i321-11+3i321−3i32-1-11-11+3i321−3i3211-1-10000-22-221+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i3000000000000001−1−i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i3200000000000000
χ594444-4-2-4-2-2-2-21−1+3i32−1−3i322-21−1+3i32−1−3i32222-2-22211−1+3i32−1−3i32−1+3i32−1−3i321-11−3i321+3i32-1-11-11−3i321+3i3211-1-100002-22-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i300000000000000-11−i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i3200000000000000
χ604444-4-2-4-2-2-2-21−1+3i32−1−3i322-21−1+3i32−1−3i32222-2-22211−1+3i32−1−3i32−1+3i32−1−3i321-11−3i321+3i32-1-11-11−3i321+3i3211-1-10000-22-221−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i3000000000000001−1+i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i3200000000000000
χ6144-4-444-44-4-41-2-2-241-2-2-211-4-1-1-1-12222221-2-2-2111222-1-1-1-100000000000000000022-2-222-2-2000000000000000000-1-111-1-1110000
χ6244-4-444-44-4-41-2-2-241-2-2-211-4-1-1-1-12222221-2-2-2111222-1-1-1-1000000000000000000-2-222-2-22200000000000000000011-1-111-1-10000
χ6344-4-444-44-4-4-21114-2111-2-2-42222-1-1-1-1-1-1-2111-2-2-2-1-1-1222200002-2-2222-2-2-2-22200000000000000-1-1-1111111-1-1-100000000000000
χ6444-4-444-44-4-4-21114-2111-2-2-42222-1-1-1-1-1-1-2111-2-2-2-1-1-122220000-222-2-2-22222-2-200000000000000111-1-1-1-1-1-111100000000000000
χ6544-4-44-2-4-222-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-222222-1-11+3i321−3i321+3i321−3i3211−1−3i32−1+3i32111-11+3i321−3i32-1-1-1-100002-2-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i300000000000000-11+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i3200000000000000
χ6644-4-44-2-4-222-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-222222-1-11+3i321−3i321+3i321−3i3211−1−3i32−1+3i32111-11+3i321−3i32-1-1-1-10000-222-21+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i3000000000000001−1−i32−1+i32-11+i321−i32-11+i321−i321−1−i32−1+i3200000000000000
χ6744-4-44-2-4-222-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-222222-1-11−3i321+3i321−3i321+3i3211−1+3i32−1−3i32111-11−3i321+3i32-1-1-1-100002-2-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i300000000000000-11−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i3200000000000000
χ6844-4-44-2-4-222-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-222222-1-11−3i321+3i321−3i321+3i3211−1+3i32−1−3i32111-11−3i321+3i32-1-1-1-10000-222-21−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i3000000000000001−1+i32−1−i32-11−i321+i32-11−i321+i321−1+i32−1−i3200000000000000
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χ968-88i−8i0-404−4i4i-42−1−3i3−1+3i304-21+3i31−3i3000−4i4i002i−2i−2ζ7+4ζ114ζ7−2ζ112ζ7−4ζ11−4ζ7+2ζ11200000-20002i−2i0000000000000000000000000000000000000000000000000000000000
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χ1018-8−8i8i0-4044i−4i-42−1−3i3−1+3i304-21+3i31−3i30004i−4i00−2i2i2ζ7−4ζ11−4ζ7+2ζ11−2ζ7+4ζ114ζ7−2ζ11200000-2000−2i2i0000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i0-4044i−4i-42−1+3i3−1−3i304-21−3i31+3i30004i−4i00−2i2i−4ζ7+2ζ112ζ7−4ζ114ζ7−2ζ11−2ζ7+4ζ11200000-2000−2i2i0000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.