Finite Group Databasebeta

← Group #13139191

Character table — Group #13139191

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666699991212121212121212181818181818181818181818181824242424242424242424363636363636363636363636363636363636363672727272
order124423461212688122424242433661212121288883666121212124444888888242424246122424242424242424224466881212121212122424242424246122424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111111-11-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111111-11-11-1-1-1-1-1-11111-1-1-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ511111111111-1-11-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ611111111111-1-11-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-111-1-1-1-11111
χ711111111111-1-11-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-111
χ811111111111-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-1
χ911-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-1ii−i−i1-11-11-1-11ii−i−ii−i11-1-1ii−i−i-11i−ii−iii−i−i11-1-111i−i-1-1ii−i−ii−i11-1-11-1i−i
χ1011-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-1ii−i−i1-11-11-1-11−i−iiii−i-1-111ii−i−i-11i−ii−iii−i−i1-1-1111−ii-1-1−i−iiii−i-1-111-11−ii
χ1111-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-1−i−iii1-11-11-1-11ii−i−i−ii-1-111−i−iii-11i−ii−iii−i−i-111-1-1-1−ii11ii−i−i−ii-1-1111-1−ii
χ1211-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-1−i−iii1-11-11-1-11−i−iii−ii11-1-1−i−iii-11i−ii−iii−i−i-1-111-1-1i−i11−i−iii−ii11-1-1-11i−i
χ1311-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-1ii−i−i1-11-11-1-11ii−i−ii−i11-1-1ii−i−i-11−ii−ii−i−iii-1-111-1-1−ii11ii−i−ii−i11-1-1-11−ii
χ1411-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-1ii−i−i1-11-11-1-11−i−iiii−i-1-111ii−i−i-11−ii−ii−i−iii-111-1-1-1i−i11−i−iiii−i-1-1111-1i−i
χ1511-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-1−i−iii1-11-11-1-11ii−i−i−ii-1-111−i−iii-11−ii−ii−i−iii1-1-1111i−i-1-1ii−i−i−ii-1-111-11i−i
χ1611-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-1−i−iii1-11-11-1-11−i−iii−ii11-1-1−i−iii-11−ii−ii−i−iii11-1-111−ii-1-1−i−iii−ii11-1-11-1−ii
χ172222222222222222222-12-1-1-1220000-12-1-1-1-1-1222220000000000-1-1-1-122-1-1-1-10202000000-1-1-1-1000000-1-100
χ182222222222222222222-12-1-1-1220000-12-1-1-1-1-12-2-2-2-20000000000-1-1-1-122-1-1-1-10-20-200000011110000001100
χ19222222222222222222-12-1222-1-10000-1-1-122-1-1-100000022220000-1-122-1-1-1-1-1-10000002200000000-1-1-1-100-1-1
χ20222222222222222222-12-1222-1-10000-1-1-122-1-1-1000000-2-2-2-20000-1-122-1-1-1-1-1-1000000-2-20000000011110011
χ2122222222222-2-22-2-2-2-22-12-1-1-1220000-12-1-1-1-1-1222220000000000-1-111-2-211110-20-2000000-1-1-1-10000001100
χ2222222222222-2-22-2-2-2-22-12-1-1-1220000-12-1-1-1-1-12-2-2-2-20000000000-1-111-2-2111102020000001111000000-1-100
χ2322222222222-2-22-2-2-2-2-12-1222-1-10000-1-1-122-1-1-100000022220000-1-1-2-2111111000000-2-200000000-1-1-1-10011
χ2422222222222-2-22-2-2-2-2-12-1222-1-10000-1-1-122-1-1-1000000-2-2-2-20000-1-1-2-21111110000002200000000111100-1-1
χ252222-22-2222-200-200002222222222222-22-2-222-20000-2-200002222-2-20000000000000000000000-2-200000000
χ262222-22-2222-200-2000022222222-2-2-2-22-22-2-222-20000220000-2-2-2-2-2-200000000000000000000002200000000
χ2722-2-222-22-2-2200-200002222-2-2-2-22i2i−2i−2i2222-2-2-2-20000−2i2i00002i2i−2i−2i2-20000000000000000000000−2i2i00000000
χ2822-2-222-22-2-2200-200002222-2-2-2-2−2i−2i2i2i2222-2-2-2-200002i−2i0000−2i−2i2i2i2-200000000000000000000002i−2i00000000
χ2922-2-2-2222-2-2-22i−2i22i2i−2i−2i2-12-111-2-20000-1-2-11-11122i2i−2i−2i00000000001-1−ii2i−2i−i−iii020-2000000−i−iii000000-1100
χ3022-2-2-2222-2-2-22i−2i22i2i−2i−2i2-12-111-2-20000-1-2-11-1112−2i−2i2i2i00000000001-1−ii2i−2i−i−iii0-202000000ii−i−i0000001-100
χ3122-2-2-2222-2-2-22i−2i22i2i−2i−2i-12-12-2-2110000-11-1-2211-100000022-2-200001-12i−2i−ii−i−iii0000002i−2i00000000-1-11100−ii
χ3222-2-2-2222-2-2-22i−2i22i2i−2i−2i-12-12-2-2110000-11-1-2211-1000000-2-22200001-12i−2i−ii−i−iii000000−2i2i0000000011-1-100i−i
χ3322-2-2-2222-2-2-2−2i2i2−2i−2i2i2i2-12-111-2-20000-1-2-11-11122i2i−2i−2i00000000001-1i−i−2i2iii−i−i0-202000000−i−iii0000001-100
χ3422-2-2-2222-2-2-2−2i2i2−2i−2i2i2i2-12-111-2-20000-1-2-11-1112−2i−2i2i2i00000000001-1i−i−2i2iii−i−i020-2000000ii−i−i000000-1100
χ3522-2-2-2222-2-2-2−2i2i2−2i−2i2i2i-12-12-2-2110000-11-1-2211-100000022-2-200001-1−2i2ii−iii−i−i000000−2i2i00000000-1-11100i−i
χ3622-2-2-2222-2-2-2−2i2i2−2i−2i2i2i-12-12-2-2110000-11-1-2211-1000000-2-22200001-1−2i2ii−iii−i−i0000002i−2i0000000011-1-100−ii
χ372-22i−2i020-22i−2i0000000022-2-22i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1320-2002i−2i01+i−1−i1−i−1+i002−2−i2i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000001+i−1−i1−i−1+i002−2−i2i20000
χ382-22i−2i020-22i−2i0000000022-2-22i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1320-2002i−2i0−1−i1+i−1+i1−i00−22i2−i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000−1−i1+i−1+i1−i00−22i2−i20000
χ392-22i−2i020-22i−2i0000000022-2-22i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1320-2002i−2i01+i−1−i1−i−1+i00−22i2−i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000001+i−1−i1−i−1+i00−22i2−i20000
χ402-22i−2i020-22i−2i0000000022-2-22i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1320-2002i−2i0−1−i1+i−1+i1−i002−2−i2i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000−1−i1+i−1+i1−i002−2−i2i20000
χ412-2−2i2i020-2−2i2i0000000022-2-2−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2320-200−2i2i01−i−1+i1+i−1−i002−2i2−i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000001−i−1+i1+i−1−i002−2i2−i20000
χ422-2−2i2i020-2−2i2i0000000022-2-2−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2320-200−2i2i0−1+i1−i−1−i1+i00−22−i2i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000−1+i1−i−1−i1+i00−22−i2i20000
χ432-2−2i2i020-2−2i2i0000000022-2-2−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2320-200−2i2i01−i−1+i1+i−1−i00−22−i2i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000001−i−1+i1+i−1−i00−22−i2i20000
χ442-2−2i2i020-2−2i2i0000000022-2-2−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2320-200−2i2i0−1+i1−i−1−i1+i002−2i2−i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000−1+i1−i−1−i1+i002−2i2−i20000
χ45444444444444444444-2-2-2-2-2-2-2-200001-21-2-211-20000000000000011-2-2-2-21111000000000000000000000000
χ4644444444444-4-44-4-4-4-4-2-2-2-2-2-2-2-200001-21-2-211-200000000000000112222-1-1-1-1000000000000000000000000
χ474444-44-4444-400-400004-24-2-2-2440000-2-4-222-2-2-4000000000000002200000000000000000000000000000000
χ484444-44-4444-400-40000-24-2444-2-20000-22-2-4-4-2-22000000000000002200000000000000000000000000000000
χ494444-44-4444-400-40000-2-2-2-2-2-2-2-200001212211200000000000000-1-100003-33-3000000000000000000000000
χ504444-44-4444-400-40000-2-2-2-2-2-2-2-200001212211200000000000000-1-10000-33-33000000000000000000000000
χ5144-4-444-44-4-4400-400004-24-222-4-40000-24-2-2222-400000000000000-2200000000000000000000000000000000
χ5244-4-444-44-4-4400-40000-24-24-4-4220000-2-2-24-422200000000000000-2200000000000000000000000000000000
χ5344-4-444-44-4-4400-40000-2-2-2-2222200001-21-22-1-12000000000000001-100003i−3i−3i3i000000000000000000000000
χ5444-4-444-44-4-4400-40000-2-2-2-2222200001-21-22-1-12000000000000001-10000−3i3i3i−3i000000000000000000000000
χ5544-4-4-4444-4-4-44i−4i44i4i−4i−4i-2-2-2-2222200001212-2-1-1-200000000000000-11−2i2i−2i2iii−i−i000000000000000000000000
χ5644-4-4-4444-4-4-4−4i4i4−4i−4i4i4i-2-2-2-2222200001212-2-1-1-200000000000000-112i−2i2i−2i−i−iii000000000000000000000000
χ574-44i−4i040-44i−4i000000004-2-42−2i2i4i−4i0000-20200−2i2i02+2i−2−2i2−2i−2+2i000000000000000000000000000000−1−i1+i−1+i1−i0000000000
χ584-44i−4i040-44i−4i000000004-2-42−2i2i4i−4i0000-20200−2i2i0−2−2i2+2i−2+2i2−2i0000000000000000000000000000001+i−1−i1−i−1+i0000000000
χ594-44i−4i040-44i−4i00000000-242-44i−4i−2i2i0000-20200−2i2i000000022−22−2i22i2000000000000000000000000000000−22i2−i20000
χ604-44i−4i040-44i−4i00000000-242-44i−4i−2i2i0000-20200−2i2i0000000−22222i2−2i20000000000000000000000000000002−2−i2i20000
χ614-4−4i4i040-4−4i4i000000004-2-422i−2i−4i4i0000-202002i−2i02−2i−2+2i2+2i−2−2i000000000000000000000000000000−1+i1−i−1−i1+i0000000000
χ624-4−4i4i040-4−4i4i000000004-2-422i−2i−4i4i0000-202002i−2i0−2+2i2−2i−2−2i2+2i0000000000000000000000000000001−i−1+i1+i−1−i0000000000
χ634-4−4i4i040-4−4i4i00000000-242-4−4i4i2i−2i0000-202002i−2i000000022−222i2−2i2000000000000000000000000000000−22−i2i20000
χ644-4−4i4i040-4−4i4i00000000-242-4−4i4i2i−2i0000-202002i−2i0000000−2222−2i22i20000000000000000000000000000002−2i2−i20000
χ6566666-36-3-3-3-366-3-3-3-3-3000000002222000000000000220000-1-1-1-100000000002020-1-100-1-10000-1-100000000
χ6666666-36-3-3-3-366-3-3-3-3-300000000-2-2-2-2000000000000-2-2000011110000000000-20-2011001100001100000000
χ6766666-36-3-3-3-3-6-6-33333000000002222000000000000220000-1-1-1-10000000000-20-201100110000-1-100000000
χ6866666-36-3-3-3-3-6-6-3333300000000-2-2-2-2000000000000-2-20000111100000000002020-1-100-1-100001100000000
χ696666-6-3-6-3-3-33003−3i33i3−3i33i3000000002222000000000000-2-20000-1-1-1-100000000000000−i3i300−i3i300001100000000
χ706666-6-3-6-3-3-33003−3i33i3−3i33i300000000-2-2-2-2000000000000220000111100000000000000i3−i300i3−i30000-1-100000000
χ716666-6-3-6-3-3-330033i3−3i33i3−3i3000000002222000000000000-2-20000-1-1-1-100000000000000i3−i300i3−i300001100000000
χ726666-6-3-6-3-3-330033i3−3i33i3−3i300000000-2-2-2-2000000000000220000111100000000000000−i3i300−i3i30000-1-100000000
χ7366-6-66-3-6-333-300333−33−3333000000002i2i−2i−2i000000000000−2i2i0000−i−iii00000000000000−i3i300i3−i30000i−i00000000
χ7466-6-66-3-6-333-300333−33−333300000000−2i−2i2i2i0000000000002i−2i0000ii−i−i00000000000000i3−i300−i3i30000−ii00000000
χ7566-6-66-3-6-333-3003−333333−33000000002i2i−2i−2i000000000000−2i2i0000−i−iii00000000000000i3−i300−i3i30000i−i00000000
χ7666-6-66-3-6-333-3003−333333−3300000000−2i−2i2i2i0000000000002i−2i0000ii−i−i00000000000000−i3i300i3−i30000−ii00000000
χ7766-6-6-6-36-33336i−6i-3−3i−3i3i3i000000002i2i−2i−2i0000000000002i−2i0000−i−iii000000000020-20-1-100110000−ii00000000
χ7866-6-6-6-36-33336i−6i-3−3i−3i3i3i00000000−2i−2i2i2i000000000000−2i2i0000ii−i−i0000000000-20201100-1-10000i−i00000000
χ7966-6-6-6-36-3333−6i6i-33i3i−3i−3i000000002i2i−2i−2i0000000000002i−2i0000−i−iii0000000000-20201100-1-10000−ii00000000
χ8066-6-6-6-36-3333−6i6i-33i3i−3i−3i00000000−2i−2i2i2i000000000000−2i2i0000ii−i−i000000000020-20-1-100110000i−i00000000
χ818-88i−8i080-88i−8i00000000-4-444−4i4i−4i4i000020-2002i−2i0000000000000000000000000000000000000000000000000
χ828-8−8i8i080-8−8i8i00000000-4-4444i−4i4i−4i000020-200−2i2i0000000000000000000000000000000000000000000000000
χ8312-1212i−12i0-606−6i6i00000000000000004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000000000
χ8412-1212i−12i0-606−6i6i0000000000000000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ130000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000000000
χ8512-12−12i12i0-6066i−6i0000000000000000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000000000
χ8612-12−12i12i0-6066i−6i00000000000000004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000000000

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