Finite Group Databasebeta

← Group #13141085

Character table — Group #13141085

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order12442346121224612336612121212612366666121212121212888824242424666612121212244488888812121212242424242424242424246122424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111-1-11111111111-1-111-1-11111-1-11111111111-11-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ61111111111-1-11111111111-1-111-1-11111-1-11111111111-11-1-1-11-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ71111111111-1-11111111111-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-11-1-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ81111111111-1-11111111111-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-111
χ911-1-1-1111-1-11-1-111111-1-1-1-11-11-1111-111-1-1-1-1ii−i−iii−i−i1-111-11-1-11-1i−ii−ii−i1-1ii−i−i11-1-1i−iii−i−i1-1i−i
χ1011-1-1-1111-1-11-1-111111-1-1-1-11-11-1111-111-1-1-1-1ii−i−iii−i−i1-111-11-1-1-11−iii−i−ii-11−i−iii-1-111i−iii−i−i-11−ii
χ1111-1-1-1111-1-11-1-111111-1-1-1-11-11-1111-111-1-1-1-1−i−iii−i−iii1-111-11-1-11-1−ii−ii−ii1-1−i−iii11-1-1−ii−i−iii1-1−ii
χ1211-1-1-1111-1-11-1-111111-1-1-1-11-11-1111-111-1-1-1-1−i−iii−i−iii1-111-11-1-1-11i−i−iii−i-11ii−i−i-1-111−ii−i−iii-11i−i
χ1311-1-1-1111-1-1-11-111111-1-1-1-1-111-1-1-11-11111-1-1ii−i−iii−i−i-1-1-1-111111-1−ii−iii−i-11−i−iii-1-111i−i−i−iii1-1i−i
χ1411-1-1-1111-1-1-11-111111-1-1-1-1-111-1-1-11-11111-1-1ii−i−iii−i−i-1-1-1-11111-11i−i−ii−ii1-1ii−i−i11-1-1i−i−i−iii-11−ii
χ1511-1-1-1111-1-1-11-111111-1-1-1-1-111-1-1-11-11111-1-1−i−iii−i−iii-1-1-1-111111-1i−ii−i−ii-11ii−i−i-1-111−iiii−i−i1-1−ii
χ1611-1-1-1111-1-1-11-111111-1-1-1-1-111-1-1-11-11111-1-1−i−iii−i−iii-1-1-1-11111-11−iii−ii−i1-1−i−iii11-1-1−iiii−i−i-11i−i
χ17222222222222222-12-122-1-122-1-1-1-1-122-1-1-1-1-12222-1-1-1-12-1-1-12-1-1-1000022000000000000-1-1-1-1-1-10000
χ18222222222222222-12-122-1-122-1-1-1-1-122-1-1-1-1-1-2-2-2-211112-1-1-12-1-1-10000-2-20000000000001111110000
χ1922222222222222-12-12-1-12222-1222-1-1-1222-1-100000000-1-1-1-1-1-1-1-10022002200-1-1-1-1000000000000-1-1
χ2022222222222222-12-12-1-12222-1222-1-1-1222-1-100000000-1-1-1-1-1-1-1-100-2-200-2-200111100000000000011
χ212222222222-2-2222-12-122-1-1-2-2-1-111-122-111-1-12222-1-1-1-1-2-111-2-1110000-2-2000000000000-1-111110000
χ222222222222-2-2222-12-122-1-1-2-2-1-111-122-111-1-1-2-2-2-21111-2-111-2-11100002200000000000011-1-1-1-10000
χ232222222222-2-222-12-12-1-122-2-2-12-2-2-1-1-12-2-2-1-1000000001-1111-111002200-2-200-1-1-1-100000000000011
χ242222222222-2-222-12-12-1-122-2-2-12-2-2-1-1-12-2-2-1-1000000001-1111-11100-2-20022001111000000000000-1-1
χ252222-22-222200-2-222222222002-2002-2-2-200222-22-222220-2000-200000000000000000000-2-200000000
χ262222-22-222200-2-222222222002-2002-2-2-20022-22-22-2-2-2-20-2000-2000000000000000000002200000000
χ272222-22-222200-2-22-12-122-1-100-11−i3i3-1-2-21−i3i3-1-12-22-2-1-1-1-101−i3i301−i3i300000000000000000011−i3i3−i3i30000
χ282222-22-222200-2-22-12-122-1-100-11−i3i3-1-2-21−i3i3-1-1-22-22111101−i3i301−i3i3000000000000000000-1-1i3−i3i3−i30000
χ292222-22-222200-2-22-12-122-1-100-11i3−i3-1-2-21i3−i3-1-12-22-2-1-1-1-101i3−i301i3−i300000000000000000011i3−i3i3−i30000
χ302222-22-222200-2-22-12-122-1-100-11i3−i3-1-2-21i3−i3-1-1-22-22111101i3−i301i3−i3000000000000000000-1-1−i3i3−i3i30000
χ3122-2-222-22-2-2002-22222-2-2-2-200220022-2-200-2-22i−2i−2i2i2i2i−2i−2i02000-200000000000000000000−2i2i00000000
χ3222-2-222-22-2-2002-22222-2-2-2-200220022-2-200-2-2−2i2i2i−2i−2i−2i2i2i02000-2000000000000000000002i−2i00000000
χ3322-2-222-22-2-2002-22-12-1-2-21100-1-1−i3i3-12-21i3−i3112i−2i−2i2i−i−iii0-1−i3i301i3−i3000000000000000000i−i3−3−330000
χ3422-2-222-22-2-2002-22-12-1-2-21100-1-1−i3i3-12-21i3−i311−2i2i2i−2iii−i−i0-1−i3i301i3−i3000000000000000000−ii−333−30000
χ3522-2-222-22-2-2002-22-12-1-2-21100-1-1i3−i3-12-21−i3i3112i−2i−2i2i−i−iii0-1i3−i301−i3i3000000000000000000i−i−333−30000
χ3622-2-222-22-2-2002-22-12-1-2-21100-1-1i3−i3-12-21−i3i311−2i2i2i−2iii−i−i0-1i3−i301−i3i3000000000000000000−ii3−3−330000
χ3722-2-2-2222-2-22-2-222-12-1-2-2112-2-11-1-1-1-22-111112i2i−2i−2i−i−iii21-1-1-2-11100002i−2i000000000000−ii−i−iii0000
χ3822-2-2-2222-2-22-2-222-12-1-2-2112-2-11-1-1-1-22-11111−2i−2i2i2iii−i−i21-1-1-2-1110000−2i2i000000000000i−iii−i−i0000
χ3922-2-2-2222-2-22-2-22-12-1211-2-22-2-1-222-11-12-2-21100000000-11-1-11-111002i−2i002i−2i00−i−iii000000000000−ii
χ4022-2-2-2222-2-22-2-22-12-1211-2-22-2-1-222-11-12-2-21100000000-11-1-11-11100−2i2i00−2i2i00ii−i−i000000000000i−i
χ4122-2-2-2222-2-2-22-222-12-1-2-211-22-1111-1-22-1-1-1112i2i−2i−2i−i−iii-21112-1-1-10000−2i2i000000000000−iiii−i−i0000
χ4222-2-2-2222-2-2-22-222-12-1-2-211-22-1111-1-22-1-1-111−2i−2i2i2iii−i−i-21112-1-1-100002i−2i000000000000i−i−i−iii0000
χ4322-2-2-2222-2-2-22-22-12-1211-2-2-22-1-2-2-2-11-122211000000001111-1-1-1-1002i−2i00−2i2i00−i−iii000000000000i−i
χ4422-2-2-2222-2-2-22-22-12-1211-2-2-22-1-2-2-2-11-122211000000001111-1-1-1-100−2i2i002i−2i00ii−i−i000000000000−ii
χ4544444444444444-2-2-2-2-2-2-2-2441-2-2-21-2-2-2-2-21100000000-2111-21110000000000000000000000000000
χ464444444444-4-444-2-2-2-2-2-2-2-2-4-41-2221-2-2-222110000000021-1-121-1-10000000000000000000000000000
χ474444-44-444400-4-4-24-24-2-24400-2-400-222-400-2-200000000020002000000000000000000000000000000
χ484444-44-444400-4-4-2-2-2-2-2-2-2-20012−2i32i31222−2i32i311000000000-1i3−i30-1i3−i30000000000000000000000000000
χ494444-44-444400-4-4-2-2-2-2-2-2-2-200122i3−2i312222i3−2i311000000000-1−i3i30-1−i3i30000000000000000000000000000
χ5044-4-444-44-4-4004-4-24-2422-4-400-2400-2-22-40022000000000-20002000000000000000000000000000000
χ5144-4-444-44-4-4004-4-2-2-2-22222001-2−2i32i31-2222i3−2i3-1-10000000001i3−i30-1−i3i30000000000000000000000000000
χ5244-4-444-44-4-4004-4-2-2-2-22222001-22i3−2i31-222−2i32i3-1-10000000001−i3i30-1i3−i30000000000000000000000000000
χ5344-4-4-4444-4-44-4-44-2-2-2-222224-412-2-212-2-222-1-100000000-2-11121-1-10000000000000000000000000000
χ5444-4-4-4444-4-4-44-44-2-2-2-22222-44122212-2-2-2-2-1-1000000002-1-1-1-21110000000000000000000000000000
χ554-44i−4i040-44i−4i000044-4-44i−4i4i−4i004000-4000004i−4i00000000000000000000000000000000000000000000
χ564-44i−4i040-44i−4i00004-2-424i−4i−2i2i00-2000200000−2i2i0000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000000000
χ574-44i−4i040-44i−4i00004-2-424i−4i−2i2i00-2000200000−2i2i00002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000000000
χ584-44i−4i040-44i−4i0000-242-4−2i2i4i−4i00-2000200000−2i2i00000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000
χ594-44i−4i040-44i−4i0000-242-4−2i2i4i−4i00-2000200000−2i2i00000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000
χ604-4−4i4i040-4−4i4i000044-4-4−4i4i−4i4i004000-400000−4i4i00000000000000000000000000000000000000000000
χ614-4−4i4i040-4−4i4i00004-2-42−4i4i2i−2i00-20002000002i−2i00002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000000000
χ624-4−4i4i040-4−4i4i00004-2-42−4i4i2i−2i00-20002000002i−2i0000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000000000
χ634-4−4i4i040-4−4i4i0000-242-42i−2i−4i4i00-20002000002i−2i00000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000
χ644-4−4i4i040-4−4i4i0000-242-42i−2i−4i4i00-20002000002i−2i00000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000
χ6566666-36-3-3-366-3-300000000-3-3000000000000000000000000000022000000220000-1-1-1-1000000-1-100
χ6666666-36-3-3-366-3-300000000-3-30000000000000000000000000000-2-2000000-2-2000011110000001100
χ6766666-36-3-3-3-6-6-3-30000000033000000000000000000000000000022000000-2-200001111000000-1-100
χ6866666-36-3-3-3-6-6-3-300000000330000000000000000000000000000-2-2000000220000-1-1-1-10000001100
χ6966-6-6-6-36-3336-63-300000000-3300000000000000000000000000002-20000002-20000-1-111000000-1100
χ7066-6-6-6-36-3336-63-300000000-330000000000000000000000000000-22000000-22000011-1-10000001-100
χ7166-6-6-6-36-333-663-3000000003-300000000000000000000000000002-2000000-22000011-1-1000000-1100
χ7266-6-6-6-36-333-663-3000000003-30000000000000000000000000000-220000002-20000-1-1110000001-100
χ738-88i−8i080-88i−8i0000-4-444−4i4i−4i4i002000-2000002i−2i00000000000000000000000000000000000000000000
χ748-8−8i8i080-8−8i8i0000-4-4444i−4i4i−4i002000-200000−2i2i00000000000000000000000000000000000000000000
χ7512121212-12-6-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-1212-6-12-66600-66000000000000000000000000000000000000000000000000000000000000000000
χ7712-1212i−12i0-606−6i6i00000000000000000000000000000000000000000000000000000000i6−i66−60000000000
χ7812-1212i−12i0-606−6i6i00000000000000000000000000000000000000000000000000000000−i6i6−660000000000
χ7912-12−12i12i0-6066i−6i00000000000000000000000000000000000000000000000000000000i6−i6−660000000000
χ8012-12−12i12i0-6066i−6i00000000000000000000000000000000000000000000000000000000−i6i66−60000000000

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