Finite Group Databasebeta

← Group #13139188

Character table — Group #13139188

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444466666666881212121212121212121212121818181818181818242424242424242436363636363636363636363636363636363636363636363672727272
order124423461212688123366121212122424366612121212242424248888242424246122424242424242244446688881212121212122424242424246122424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-11-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ511111111111-1-1111111111-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111
χ611111111111-1-1111111111-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1111111-1-1-1-1
χ711111111111-1-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-1111111-1-1
χ811111111111-1-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11-1111111-1-1111111-1-1-1-1-1-1-1-111
χ911-1-1-1111-1-1-1i−i11111-1-1-1-1i−i1-1-111-1-11ii−i−iii−i−iii−i−i-11i−iii−i−i11-1-1i−i11i−i1-1ii−i−i-1-1i−i11-1-11-1i−i
χ1011-1-1-1111-1-1-1i−i11111-1-1-1-1i−i1-1-111-1-11ii−i−iii−i−iii−i−i-11i−iii−i−i1-1-11−ii11−ii-11−i−iii-1-1i−i-1-111-11−ii
χ1111-1-1-1111-1-1-1i−i11111-1-1-1-1i−i1-1-111-1-11ii−i−i−i−iii−i−iii-11i−iii−i−i-111-1i−i-1-1−ii-11ii−i−i11−ii-1-1111-1−ii
χ1211-1-1-1111-1-1-1i−i11111-1-1-1-1i−i1-1-111-1-11ii−i−i−i−iii−i−iii-11i−iii−i−i-1-111−ii-1-1i−i1-1−i−iii11−ii11-1-1-11i−i
χ1311-1-1-1111-1-1-1−ii11111-1-1-1-1−ii1-1-111-1-11−i−iiiii−i−iii−i−i-11−ii−i−iii-111-1−ii-1-1i−i-11−i−iii11i−i-1-1111-1i−i
χ1411-1-1-1111-1-1-1−ii11111-1-1-1-1−ii1-1-111-1-11−i−iiiii−i−iii−i−i-11−ii−i−iii-1-111i−i-1-1−ii1-1ii−i−i11i−i11-1-1-11−ii
χ1511-1-1-1111-1-1-1−ii11111-1-1-1-1−ii1-1-111-1-11−i−iii−i−iii−i−iii-11−ii−i−iii11-1-1−ii11−ii1-1−i−iii-1-1−ii11-1-11-1−ii
χ1611-1-1-1111-1-1-1−ii11111-1-1-1-1−ii1-1-111-1-11−i−iii−i−iii−i−iii-11−ii−i−iii1-1-11i−i11i−i-11ii−i−i-1-1−ii-1-111-11i−i
χ17222222222222222-12-122-1-122-12-1-1-1-1-12-1-1-1-12222-1-1-1-1-1-122-1-1-1-1202000-1-100000000-1-1-1-100000000
χ18222222222222222-12-122-1-122-12-1-1-1-1-12-1-1-1-1-2-2-2-21111-1-122-1-1-1-1-20-20001100000000111100000000
χ1922222222222222-12-12-1-12222-1-12-12-1-1-1222200000000-1-1-1-1-1-1-1-100000000222200000000-1-1-1-100-1-1
χ2022222222222222-12-12-1-12222-1-12-12-1-1-1222200000000-1-1-1-1-1-1-1-100000000-2-2-2-20000000011110011
χ2122222222222-2-222-12-122-1-1-2-2-12-1-1-1-1-1211112222-1-1-1-1-1-1-2-21111-20-2000110000000011-1-100000000
χ2222222222222-2-222-12-122-1-1-2-2-12-1-1-1-1-121111-2-2-2-21111-1-1-2-21111202000-1-100000000-1-11100000000
χ2322222222222-2-22-12-12-1-122-2-2-1-12-12-1-1-1-2-2-2-200000000-1-11111110000000022-2-200000000111100-1-1
χ2422222222222-2-22-12-12-1-122-2-2-1-12-12-1-1-1-2-2-2-200000000-1-111111100000000-2-22200000000-1-1-1-10011
χ252222-22-2222-200-222222222002-2-22-222-200002-22-22222-2-2000000000000000000000000-2-200000000
χ262222-22-2222-200-222222222002-2-22-222-20000-22-22-2-2-2-2-2-20000000000000000000000002200000000
χ272222-22-2222-200-22-12-122-1-100-1-21-11-1-1-2−i3i3−i3i32-22-2-1-1-1-11100−i3i3−i3i3000000−i3i300000000−i3i31100000000
χ282222-22-2222-200-22-12-122-1-100-1-21-11-1-1-2−i3i3−i3i3-22-2211111100−i3i3−i3i3000000i3−i300000000i3−i3-1-100000000
χ292222-22-2222-200-22-12-122-1-100-1-21-11-1-1-2i3−i3i3−i32-22-2-1-1-1-11100i3−i3i3−i3000000i3−i300000000i3−i31100000000
χ302222-22-2222-200-22-12-122-1-100-1-21-11-1-1-2i3−i3i3−i3-22-2211111100i3−i3i3−i3000000−i3i300000000−i3i3-1-100000000
χ3122-2-222-22-2-2200-22222-2-2-2-2002222-2-2-2-200002i−2i−2i2i2i2i−2i−2i2-2000000000000000000000000−2i2i00000000
χ3222-2-222-22-2-2200-22222-2-2-2-2002222-2-2-2-20000−2i2i2i−2i−2i−2i2i2i2-20000000000000000000000002i−2i00000000
χ3322-2-222-22-2-2200-22-12-1-2-21100-12-1-1111-23−3−332i−2i−2i2i−i−iii-11003−3−33000000−i3i300000000i3−i3i−i00000000
χ3422-2-222-22-2-2200-22-12-1-2-21100-12-1-1111-23−3−33−2i2i2i−2iii−i−i-11003−3−33000000i3−i300000000−i3i3−ii00000000
χ3522-2-222-22-2-2200-22-12-1-2-21100-12-1-1111-2−333−32i−2i−2i2i−i−iii-1100−333−3000000i3−i300000000−i3i3i−i00000000
χ3622-2-222-22-2-2200-22-12-1-2-21100-12-1-1111-2−333−3−2i2i2i−2iii−i−i-1100−333−3000000−i3i300000000i3−i3−ii00000000
χ3722-2-2-2222-2-2-22i−2i22-12-1-2-2112i−2i-1-21-1-1112−i−iii2i2i−2i−2i−i−iii1-12i−2i−i−iii20-2000-1-10000000011−ii00000000
χ3822-2-2-2222-2-2-22i−2i22-12-1-2-2112i−2i-1-21-1-1112−i−iii−2i−2i2i2iii−i−i1-12i−2i−i−iii-2020001100000000-1-1i−i00000000
χ3922-2-2-2222-2-2-22i−2i2-12-1211-2-22i−2i-11-2-1211-12i2i−2i−2i000000001-1−ii−i−iii000000002i−2i2-200000000-1-11100−ii
χ4022-2-2-2222-2-2-22i−2i2-12-1211-2-22i−2i-11-2-1211-12i2i−2i−2i000000001-1−ii−i−iii00000000−2i2i-220000000011-1-100i−i
χ4122-2-2-2222-2-2-2−2i2i22-12-1-2-211−2i2i-1-21-1-1112ii−i−i2i2i−2i−2i−i−iii1-1−2i2iii−i−i-2020001100000000-1-1−ii00000000
χ4222-2-2-2222-2-2-2−2i2i22-12-1-2-211−2i2i-1-21-1-1112ii−i−i−2i−2i2i2iii−i−i1-1−2i2iii−i−i20-2000-1-10000000011i−i00000000
χ4322-2-2-2222-2-2-2−2i2i2-12-1211-2-2−2i2i-11-2-1211-1−2i−2i2i2i000000001-1i−iii−i−i000000002i−2i-220000000011-1-100−ii
χ4422-2-2-2222-2-2-2−2i2i2-12-1211-2-2−2i2i-11-2-1211-1−2i−2i2i2i000000001-1i−iii−i−i00000000−2i2i2-200000000-1-11100i−i
χ4544444444444444-2-2-2-2-2-2-2-2441-2-21-211-2-2-2-2-20000000011-2-211110000000000000000000000000000
χ4644444444444-4-44-2-2-2-2-2-2-2-2-4-41-2-21-211-22222000000001122-1-1-1-10000000000000000000000000000
χ474444-44-4444-400-4-24-24-2-24400-22-4-2-4-2-22000000000000220000000000000000000000000000000000
χ484444-44-4444-400-4-2-2-2-2-2-2-2-20012212112−2i32i3−2i32i300000000-1-100i3−i3i3−i30000000000000000000000000000
χ494444-44-4444-400-4-2-2-2-2-2-2-2-200122121122i3−2i32i3−2i300000000-1-100−i3i3−i3i30000000000000000000000000000
χ5044-4-444-44-4-4400-4-24-2422-4-400-2-24-2-4222000000000000-220000000000000000000000000000000000
χ5144-4-444-44-4-4400-4-2-2-2-22222001-2-212-1-1223−23−2323000000001-100−333−30000000000000000000000000000
χ5244-4-444-44-4-4400-4-2-2-2-22222001-2-212-1-12−232323−23000000001-1003−3−330000000000000000000000000000
χ5344-4-4-4444-4-4-44i−4i4-2-2-2-222224i−4i1221-2-1-1-2−2i−2i2i2i00000000-11−2i2iii−i−i0000000000000000000000000000
χ5444-4-4-4444-4-4-4−4i4i4-2-2-2-22222−4i4i1221-2-1-1-22i2i−2i−2i00000000-112i−2i−i−iii0000000000000000000000000000
χ554-44i−4i040-44i−4i000044-4-44i−4i4i−4i00400-404i−4i0000000000000000000000000000000000000000000000000
χ564-44i−4i040-44i−4i00004-2-424i−4i−2i2i00-20020−2i2i000000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000000000
χ574-44i−4i040-44i−4i00004-2-424i−4i−2i2i00-20020−2i2i0000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000000000
χ584-44i−4i040-44i−4i0000-242-4−2i2i4i−4i00-20020−2i2i000000000000000000000000000000000000000006−6i6−i60000
χ594-44i−4i040-44i−4i0000-242-4−2i2i4i−4i00-20020−2i2i00000000000000000000000000000000000000000−66−i6i60000
χ604-4−4i4i040-4−4i4i000044-4-4−4i4i−4i4i00400-40−4i4i0000000000000000000000000000000000000000000000000
χ614-4−4i4i040-4−4i4i00004-2-42−4i4i2i−2i00-200202i−2i0000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000000000
χ624-4−4i4i040-4−4i4i00004-2-42−4i4i2i−2i00-200202i−2i000000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000000000
χ634-4−4i4i040-4−4i4i0000-242-42i−2i−4i4i00-200202i−2i000000000000000000000000000000000000000006−6−i6i60000
χ644-4−4i4i040-4−4i4i0000-242-42i−2i−4i4i00-200202i−2i00000000000000000000000000000000000000000−66i6−i60000
χ6566666-36-3-3-3-366-300000000-3-30000000000000000000000000000020222000000-1-1-1-100000000-1-100
χ6666666-36-3-3-3-366-300000000-3-300000000000000000000000000000-20-2-2-20000001111000000001100
χ6766666-36-3-3-3-3-6-6-3000000003300000000000000000000000000000202-2-2000000111100000000-1-100
χ6866666-36-3-3-3-3-6-6-3000000003300000000000000000000000000000-20-222000000-1-1-1-1000000001100
χ6966-6-6-6-36-33336i−6i-300000000−3i3i0000000000000000000000000000020-22i−2i000000−i−iii00000000-1100
χ7066-6-6-6-36-33336i−6i-300000000−3i3i00000000000000000000000000000-202−2i2i000000ii−i−i000000001-100
χ7166-6-6-6-36-3333−6i6i-3000000003i−3i0000000000000000000000000000020-2−2i2i000000ii−i−i00000000-1100
χ7266-6-6-6-36-3333−6i6i-3000000003i−3i00000000000000000000000000000-2022i−2i000000−i−iii000000001-100
χ738-88i−8i080-88i−8i0000-4-444−4i4i−4i4i00200-202i−2i0000000000000000000000000000000000000000000000000
χ748-8−8i8i080-8−8i8i0000-4-4444i−4i4i−4i00200-20−2i2i0000000000000000000000000000000000000000000000000
χ7512121212-12-6-12-6-6-66006000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-1212-6-12-666-6006000000000000000000000000000000000000000000000000000000000000000000
χ7712-1212i−12i0-606−6i6i000000000000000000000000000000000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000
χ7812-1212i−12i0-606−6i6i000000000000000000000000000000000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000
χ7912-12−12i12i0-6066i−6i000000000000000000000000000000000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000
χ8012-12−12i12i0-6066i−6i000000000000000000000000000000000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000

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