Finite Group Databasebeta

← Group #13167078

Character table — Group #13167078

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size111122222244444444444444444444448888888888888818182424242424242424242424242424242424243636363636363636363636363636363636108108108108
order12223446663333666666666666121212121212366612121212121212121212444412121212121212121212121212121212444441212121212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111
χ511111-1-11111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-111-1-1111111-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111-1-1
χ611111-1-11111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-111-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111
χ711111-1-11111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1-1-111111111-1-1-111-1-11111-1-1-1-1-1-111
χ811111-1-11111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-1111111-1-1
χ92222222222222222222222222222222222222222222222-2-200000000000000000000-200-2-2-2-2000000000000
χ1022222-2-22222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000200-2-222000000000000
χ112222-122-1-1-122-1-12-1-122-1-12-1-122-1-12222-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-100200-1-1-1-1000000000000
χ122222-122-1-1-122-1-12-1-122-1-12-1-122-1-12222-1-1-1-122-1-1-1-1-1-1-1-122-2-21111-2-21111-2-2111100200-1-1-1-1000000000000
χ132222-122-1-1-122-1-12-1-122-1-12-1-122-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-2-200−i3i3−i3i300−i3−i3i3i300−i3−i3i3i300-2001111000000000000
χ142222-122-1-1-122-1-12-1-122-1-12-1-122-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-2-200i3−i3i3−i300i3i3−i3−i300i3i3−i3−i300-2001111000000000000
χ152222-1-2-2-1-1-122-1-12-1-122-1-12-1-12211-2-2-2-2-1-1-1-1-2-211111111222-2-1-11122-1-1-1-1-2-2111100-200-1-111000000000000
χ162222-1-2-2-1-1-122-1-12-1-122-1-12-1-12211-2-2-2-2-1-1-1-1-2-21111111122-2211-1-1-2-2111122-1-1-1-100-200-1-111000000000000
χ172222-1-2-2-1-1-122-1-12-1-122-1-12-1-12211-2-2-2-2-1-1-1-1-2-211111111-2-200−i3i3i3−i300−i3−i3i3i300i3i3−i3−i30020011-1-1000000000000
χ182222-1-2-2-1-1-122-1-12-1-122-1-12-1-12211-2-2-2-2-1-1-1-1-2-211111111-2-200i3−i3−i3i300i3i3−i3−i300−i3−i3i3i30020011-1-1000000000000
χ1922-2-222-22-2-22222-2-2-22222-2-2-2-2-22-222-2-22-2-222-222-2-222-2-200000000000000000000000000000000000002−22−2
χ2022-2-222-22-2-22222-2-2-22222-2-2-2-2-22-222-2-22-2-222-222-2-222-2-20000000000000000000000000000000000000−22−22
χ2122-2-22-222-2-22222-2-2-22222-2-2-2-2-2-22-2-2222-2-22-22-2-222-2-22200000000000000000000000000000000000002−2−22
χ2222-2-22-222-2-22222-2-2-22222-2-2-2-2-2-22-2-2222-2-22-22-2-222-2-2220000000000000000000000000000000000000−222−2
χ232-22-2200-22-22222222-2-2-2-2-2-2-22-200000022-2-200000000002-20000000000000000002-20002-20022-2-200000000
χ242-22-2200-22-22222222-2-2-2-2-2-2-22-200000022-2-200000000002-2000000000000000000-220002-200-2-22200000000
χ252-22-2200-22-22222222-2-2-2-2-2-2-22-200000022-2-20000000000-220000000000000000000002i−2i-220000002i2i−2i−2i0000
χ262-22-2200-22-22222222-2-2-2-2-2-2-22-200000022-2-20000000000-22000000000000000000000−2i2i-22000000−2i−2i2i2i0000
χ2744444444441-2111111-211111-2-244-2-2-2-2-2-2-2-2111111-2-2-2-200222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000
χ2844444444441-2111111-211111-2-244-2-2-2-2-2-2-2-2111111-2-2-2-200-2-2-2-2-2-2111111111111000000000000000000000
χ294444444444-21-2-2-2-2-2-21-2-2-2-2-2114411111111-2-2-2-2-2-2111100000000000000000000220220000-1-1-1-1-1-1-1-10000
χ304444444444-21-2-2-2-2-2-21-2-2-2-2-2114411111111-2-2-2-2-2-2111100000000000000000000-2-20-2-20000111111110000
χ3144444-4-44441-2111111-211111-2-2-4-42222-2-2-2-2-1-1-1-1-1-12222002-222-2-2-1-1-1-1-1-1111111000000000000000000000
χ3244444-4-44441-2111111-211111-2-2-4-42222-2-2-2-2-1-1-1-1-1-1222200-22-2-222111111-1-1-1-1-1-1000000000000000000000
χ3344444-4-4444-21-2-2-2-2-2-21-2-2-2-2-211-4-4-1-1-1-11111222222-1-1-1-100000000000000000000220-2-20000-1-1-1-111110000
χ3444444-4-4444-21-2-2-2-2-2-21-2-2-2-2-211-4-4-1-1-1-11111222222-1-1-1-100000000000000000000-2-202200001111-1-1-1-10000
χ354444-244-2-2-21-2−1−3i32−1+3i321−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-2-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i3211110022−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000000000000
χ364444-244-2-2-21-2−1−3i32−1+3i321−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-2-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111100-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000000000000
χ374444-244-2-2-21-2−1+3i32−1−3i321−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-2-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i3211110022−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000000000000
χ384444-244-2-2-21-2−1+3i32−1−3i321−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-2-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32111100-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000000000000
χ394444-2-4-4-2-2-21-2−1−3i32−1+3i321−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2-22222221111-1-11+3i321−3i321+3i321−3i32-1-1-1-1002-2−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000000000
χ404444-2-4-4-2-2-21-2−1−3i32−1+3i321−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2-22222221111-1-11+3i321−3i321+3i321−3i32-1-1-1-100-221+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000000000
χ414444-2-4-4-2-2-21-2−1+3i32−1−3i321−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2-22222221111-1-11−3i321+3i321−3i321+3i32-1-1-1-1002-2−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000000000
χ424444-2-4-4-2-2-21-2−1+3i32−1−3i321−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2-22222221111-1-11−3i321+3i321−3i321+3i32-1-1-1-100-221−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000000000
χ4344-4-444-44-4-41-211-1-1-11-211-1-1-1224-4-2-222-222-21-111-1-1-2-222000000003−33−33−33−33−33−3000000000000000000000
χ4444-4-444-44-4-41-211-1-1-11-211-1-1-1224-4-2-222-222-21-111-1-1-2-22200000000−33−33−33−33−33−33000000000000000000000
χ4544-4-444-44-4-4-21-2-2222-21-2-2222-1-14-411-1-11-1-11-22-2-22211-1-1000000000000000000000000000003−33−33−33−30000
χ4644-4-444-44-4-4-21-2-2222-21-2-2222-1-14-411-1-11-1-11-22-2-22211-1-100000000000000000000000000000−33−33−33−330000
χ4744-4-44-444-4-41-211-1-1-11-211-1-1-122-4422-2-2-222-2-11-1-11122-2-2000000003−33−33−3−33−33−33000000000000000000000
χ4844-4-44-444-4-41-211-1-1-11-211-1-1-122-4422-2-2-222-2-11-1-11122-2-200000000−33−33−333−33−33−3000000000000000000000
χ4944-4-44-444-4-4-21-2-2222-21-2-2222-1-1-44-1-1111-1-112-222-2-2-1-111000000000000000000000000000003−33−3−33−330000
χ5044-4-44-444-4-4-21-2-2222-21-2-2222-1-1-44-1-1111-1-112-222-2-2-1-11100000000000000000000000000000−33−333−33−30000
χ5144-4-4-24-4-2221-2−1−3i32−1+3i32-11+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i3222-22-2-2221-1-111-1−1−3i32−1+3i321+3i321−3i3211-1-1000000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ223−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22000000000000000000000
χ5244-4-4-24-4-2221-2−1−3i32−1+3i32-11+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i3222-22-2-2221-1-111-1−1−3i32−1+3i321+3i321−3i3211-1-100000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22000000000000000000000
χ5344-4-4-24-4-2221-2−1+3i32−1−3i32-11−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i3222-22-2-2221-1-111-1−1+3i32−1−3i321−3i321+3i3211-1-1000000003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ223−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22000000000000000000000
χ5444-4-4-24-4-2221-2−1+3i32−1−3i32-11−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i3222-22-2-2221-1-111-1−1+3i32−1−3i321−3i321+3i3211-1-100000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22000000000000000000000
χ5544-4-4-24-4-22244-2-2-42244-2-2-422-4-4-2244-4-4-222-24-4-2-222-2-22200000000000000000000000000000000000000000
χ5644-4-4-2-44-2221-2−1−3i32−1+3i32-11+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i32222-222-2-21-1-11-111+3i321−3i32−1−3i32−1+3i32-1-111000000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22000000000000000000000
χ5744-4-4-2-44-2221-2−1−3i32−1+3i32-11+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i32222-222-2-21-1-11-111+3i321−3i32−1−3i32−1+3i32-1-11100000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ223−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22000000000000000000000
χ5844-4-4-2-44-2221-2−1+3i32−1−3i32-11−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i32222-222-2-21-1-11-111−3i321+3i32−1+3i32−1−3i32-1-111000000003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22000000000000000000000
χ5944-4-4-2-44-2221-2−1+3i32−1−3i32-11−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i32222-222-2-21-1-11-111−3i321+3i32−1+3i32−1−3i32-1-11100000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ223−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22000000000000000000000
χ6044-4-4-2-44-22244-2-2-42244-2-2-422-4-42-2-4-444-222-2-4422-2-222-2-200000000000000000000000000000000000000000
χ614-44-4400-44-4-21-2-2-2-2-22-1222221-1003i−3i3i−3i11-1-10000003i−3i3i−3i000000000000000000002-202i−2i0000-1-111−i−iii0000
χ624-44-4400-44-4-21-2-2-2-2-22-1222221-1003i−3i3i−3i11-1-10000003i−3i3i−3i00000000000000000000-220−2i2i000011-1-1ii−i−i0000
χ634-44-4400-44-4-21-2-2-2-2-22-1222221-100−3i3i−3i3i11-1-1000000−3i3i−3i3i000000000000000000002-20−2i2i0000-1-111ii−i−i0000
χ644-44-4400-44-4-21-2-2-2-2-22-1222221-100−3i3i−3i3i11-1-1000000−3i3i−3i3i00000000000000000000-2202i−2i000011-1-1−i−iii0000
χ654-44-4-2002-2244-2-24-2-2-4-422-4224-4000000-2-22200000000004-400000000000000000000000-2200000000000000
χ664-44-4-2002-2244-2-24-2-2-4-422-4224-4000000-2-2220000000000-44000000000000000000000002-200000000000000
χ674-4-44400-4-444444-4-4-4-4-4-4-4444-440000004-44-4000000000000000000000000000000000000000000000000000
χ684-4-44400-4-44-21-2-22222-122-2-2-2-11003i−3i−3i3i1-11-10000003i−3i−3i3i000000000000000000000000000003−3−33i3−i3−i3i30000
χ694-4-44400-4-44-21-2-22222-122-2-2-2-11003i−3i−3i3i1-11-10000003i−3i−3i3i00000000000000000000000000000−333−3−i3i3i3−i30000
χ704-4-44400-4-44-21-2-22222-122-2-2-2-1100−3i3i3i−3i1-11-1000000−3i3i3i−3i000000000000000000000000000003−3−33−i3i3i3−i30000
χ714-4-44400-4-44-21-2-22222-122-2-2-2-1100−3i3i3i−3i1-11-1000000−3i3i3i−3i00000000000000000000000000000−333−3i3−i3−i3i30000
χ724-4-44-20022-244-2-2-422-4-4224-2-2-44000000-22-220000000000000000000000000000000000000−2i32i3000000000000
χ734-4-44-20022-244-2-2-422-4-4224-2-2-44000000-22-2200000000000000000000000000000000000002i3−2i3000000000000
χ748888-488-4-4-4-4222-422-4222-42222-4-42222-1-1-1-1-4-42222-1-1-1-100000000000000000000000000000000000000000
χ758888-4-8-8-4-4-4-4222-422-4222-4222244-2-2-2-2-1-1-1-144-2-2-2-2111100000000000000000000000000000000000000000
χ7688-8-8-48-8-444-42224-2-2-42224-2-2-2-2-4422-2-2-111-1-4422-2-2-1-11100000000000000000000000000000000000000000
χ7788-8-8-4-88-444-42224-2-2-42224-2-2-2-24-4-2-222-111-14-4-2-22211-1-100000000000000000000000000000000000000000
χ788-88-8800-88-82-422222-24-2-2-2-2-2-44000000-4-444000000000000000000000000000000000000000000000000000
χ798-88-8-4004-442-4−1−3i3−1+3i32−1−3i3−1+3i3-241+3i31−3i3-21+3i31−3i3-4400000022-2-2000000000000000000000000000000000000000000000000000
χ808-88-8-4004-442-4−1+3i3−1−3i32−1+3i3−1−3i3-241−3i31+3i3-21−3i31+3i3-4400000022-2-2000000000000000000000000000000000000000000000000000
χ818-88-8-4004-44-4222-4224-2-2-24-2-22-2006i−6i6i−6i-1-111000000−3i3i−3i3i00000000000000000000000000000000000000000
χ828-88-8-4004-44-4222-4224-2-2-24-2-22-200−6i6i−6i6i-1-1110000003i−3i3i−3i00000000000000000000000000000000000000000
χ838-8-88800-8-882-422-2-2-2-24-2-22224-4000000-44-44000000000000000000000000000000000000000000000000000
χ848-8-88-40044-42-4−1−3i3−1+3i3-21+3i31−3i3-241+3i31−3i32−1−3i3−1+3i34-40000002-22-2000000000000000000000000000000000000000000000000000
χ858-8-88-40044-42-4−1+3i3−1−3i3-21−3i31+3i3-241−3i31+3i32−1+3i3−1−3i34-40000002-22-2000000000000000000000000000000000000000000000000000
χ868-8-88-40044-4-42224-2-24-2-2-2-422-22006i−6i−6i6i-11-11000000−3i3i3i−3i00000000000000000000000000000000000000000
χ878-8-88-40044-4-42224-2-24-2-2-2-422-2200−6i6i6i−6i-11-110000003i−3i−3i3i00000000000000000000000000000000000000000

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