Finite Group Databasebeta

← Group #11784589

Character table — Group #11784589

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111114444444444444444448888888899999999121212121212121212121212121212122424242424242424242424242424242436363636363636363636
order122244442334666666121212121212121266661212121222224444222244448888888866661212121224242424242424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ511111111-111-111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ611111111-111-111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ711111111-111-111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ811111111-111-111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1
χ91111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111ii−i−iii−i−i11-1-1-1-111ii−i−iii−i−i1-1ii−i−iii−i−i
χ101111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111−i−iii−i−iii11-1-1-1-111−i−iii−i−iii1-1−i−iii−i−iii
χ111111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1ii−i−iii−i−i-1-11111-1-1ii−i−iii−i−i1-1−i−iii−i−iii
χ121111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−iii−i−iii-1-11111-1-1−i−iii−i−iii1-1ii−i−iii−i−i
χ131111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1ii−i−i−i−iii1111-1-1-1-1ii−i−i−i−iii-11ii−i−i−i−iii
χ141111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1−i−iiiii−i−i1111-1-1-1-1−i−iiiii−i−i-11−i−iiiii−i−i
χ151111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iii-1-1-1-11111ii−i−i−i−iii-11−i−iiiii−i−i
χ161111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i-1-1-1-11111−i−iiiii−i−i-11ii−i−i−i−iii
χ172222222222222222222222222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000-2-200000000
χ1822222222-222-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000002200000000
χ192222-2-2-2-2222-2222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000-2200000000
χ202222-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000002-200000000
χ2122-2-22i2i−2i−2i02202-22-2-2-22i2i−2i−2i2i2i−2i−2i0000000022-2-22i2i−2i−2i000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ2222-2-22i2i−2i−2i02202-22-2-2-22i2i−2i−2i2i2i−2i−2i0000000022-2-22i2i−2i−2i00000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ2322-2-22i2i−2i−2i02202-22-2-2-22i2i−2i−2i2i2i−2i−2i00000000-2-222−2i−2i2i2i00000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ2422-2-22i2i−2i−2i02202-22-2-2-22i2i−2i−2i2i2i−2i−2i00000000-2-222−2i−2i2i2i0000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ2522-2-2−2i−2i2i2i02202-22-2-2-2−2i−2i2i2i−2i−2i2i2i0000000022-2-2−2i−2i2i2i000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ2622-2-2−2i−2i2i2i02202-22-2-2-2−2i−2i2i2i−2i−2i2i2i0000000022-2-2−2i−2i2i2i00000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ2722-2-2−2i−2i2i2i02202-22-2-2-2−2i−2i2i2i−2i−2i2i2i00000000-2-2222i2i−2i−2i00000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ2822-2-2−2i−2i2i2i02202-22-2-2-2−2i−2i2i2i−2i−2i2i2i00000000-2-2222i2i−2i−2i0000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ292-22-22i−2i2i−2i0220-22-22-2-22i−2i2i−2i2i−2i2i−2i000000002-22-22i−2i2i−2i0000000000002ζ−2ζ2ζ3−2ζ30000000000002ζ−2ζ2ζ3−2ζ30000000000
χ302-22-22i−2i2i−2i0220-22-22-2-22i−2i2i−2i2i−2i2i−2i000000002-22-22i−2i2i−2i000000000000−2ζ2ζ−2ζ32ζ3000000000000−2ζ2ζ−2ζ32ζ30000000000
χ312-22-22i−2i2i−2i0220-22-22-2-22i−2i2i−2i2i−2i2i−2i00000000-22-22−2i2i−2i2i000000002ζ−2ζ2ζ3−2ζ30000000000002ζ−2ζ2ζ3−2ζ300000000000000
χ322-22-22i−2i2i−2i0220-22-22-2-22i−2i2i−2i2i−2i2i−2i00000000-22-22−2i2i−2i2i00000000−2ζ2ζ−2ζ32ζ3000000000000−2ζ2ζ−2ζ32ζ300000000000000
χ332-22-2−2i2i−2i2i0220-22-22-2-2−2i2i−2i2i−2i2i−2i2i000000002-22-2−2i2i−2i2i0000000000002ζ3−2ζ32ζ−2ζ0000000000002ζ3−2ζ32ζ−2ζ0000000000
χ342-22-2−2i2i−2i2i0220-22-22-2-2−2i2i−2i2i−2i2i−2i2i000000002-22-2−2i2i−2i2i000000000000−2ζ32ζ3−2ζ2ζ000000000000−2ζ32ζ3−2ζ2ζ0000000000
χ352-22-2−2i2i−2i2i0220-22-22-2-2−2i2i−2i2i−2i2i−2i2i00000000-22-222i−2i2i−2i000000002ζ3−2ζ32ζ−2ζ0000000000002ζ3−2ζ32ζ−2ζ00000000000000
χ362-22-2−2i2i−2i2i0220-22-22-2-2−2i2i−2i2i−2i2i−2i2i00000000-22-222i−2i2i−2i00000000−2ζ32ζ3−2ζ2ζ000000000000−2ζ32ζ3−2ζ2ζ00000000000000
χ372-2-222-2-220220-2-2-2-2222-2-222-2-22000000002-2-222-2-222-2002-200000000002-2002-200000000000000000000
χ382-2-222-2-220220-2-2-2-2222-2-222-2-22000000002-2-222-2-22-2200-220000000000-2200-2200000000000000000000
χ392-2-222-2-220220-2-2-2-2222-2-222-2-2200000000-222-2-222-2002-2002-200000000002-2002-2000000000000000000
χ402-2-222-2-220220-2-2-2-2222-2-222-2-2200000000-222-2-222-200-2200-220000000000-2200-22000000000000000000
χ412-2-22-222-20220-2-2-2-222-222-2-222-2000000002-2-22-222-22-200-2200000000002-200-2200000000000000000000
χ422-2-22-222-20220-2-2-2-222-222-2-222-2000000002-2-22-222-2-22002-20000000000-22002-200000000000000000000
χ432-2-22-222-20220-2-2-2-222-222-2-222-200000000-222-22-2-22002-200-2200000000002-200-22000000000000000000
χ442-2-22-222-20220-2-2-2-222-222-2-222-200000000-222-22-2-2200-22002-20000000000-22002-2000000000000000000
χ454444444441-2411-2-21-2-2-2-2-2111111-2-211-2-200000000000000002222222200000000-1-1-1-1-1-1-1-10000000000
χ464444444441-2411-2-21-2-2-2-2-2111111-2-211-2-20000000000000000-2-2-2-2-2-2-2-200000000111111110000000000
χ47444444444-214-2-211-211111-2-2-2-2-2-211-2-211000000002222222200000000-1-1-1-1-1-1-1-1000000000000000000
χ48444444444-214-2-211-211111-2-2-2-2-2-211-2-21100000000-2-2-2-2-2-2-2-20000000011111111000000000000000000
χ4944444444-41-2-411-2-21-2-2-2-2-21111-1-122-1-12200000000000000002222-2-2-2-200000000-1-1-1-111110000000000
χ5044444444-41-2-411-2-21-2-2-2-2-21111-1-122-1-1220000000000000000-2-2-2-22222000000001111-1-1-1-10000000000
χ5144444444-4-21-4-2-211-211111-2-2-2-222-1-122-1-10000000022-2-222-2-200000000-1-111-1-111000000000000000000
χ5244444444-4-21-4-2-211-211111-2-2-2-222-1-122-1-100000000-2-222-2-2220000000011-1-111-1-1000000000000000000
χ534444-4-4-4-441-2-411-2-21-22222-1-1-1-111-2-2-1-12200000000000000002i2i−2i−2i2i2i−2i−2i00000000−i−iii−i−iii0000000000
χ544444-4-4-4-441-2-411-2-21-22222-1-1-1-111-2-2-1-1220000000000000000−2i−2i2i2i−2i−2i2i2i00000000ii−i−iii−i−i0000000000
χ554444-4-4-4-44-21-4-2-211-21-1-1-1-12222-2-21122-1-10000000022-2-2-2-22200000000-1-11111-1-1000000000000000000
χ564444-4-4-4-44-21-4-2-211-21-1-1-1-12222-2-21122-1-100000000-2-22222-2-20000000011-1-1-1-111000000000000000000
χ574444-4-4-4-4-41-2411-2-21-22222-1-1-1-1-1-12211-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000−i−iiiii−i−i0000000000
χ584444-4-4-4-4-41-2411-2-21-22222-1-1-1-1-1-12211-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000ii−i−i−i−iii0000000000
χ594444-4-4-4-4-4-214-2-211-21-1-1-1-1222222-1-1-2-211000000002222-2-2-2-200000000-1-1-1-11111000000000000000000
χ604444-4-4-4-4-4-214-2-211-21-1-1-1-1222222-1-1-2-21100000000-2-2-2-22222000000001111-1-1-1-1000000000000000000
χ614-44-44i−4i4i−4i01-20-112-2-12−2i2i−2i2ii−ii−i3-3003i−3i0000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000−ζζ−ζ3ζ3−ζζ−ζ3ζ30000000000
χ624-44-44i−4i4i−4i01-20-112-2-12−2i2i−2i2ii−ii−i3-3003i−3i000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000ζ−ζζ3−ζ3ζ−ζζ3−ζ30000000000
χ634-44-44i−4i4i−4i01-20-112-2-12−2i2i−2i2ii−ii−i-3300−3i3i0000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ300000000−ζζ−ζ3ζ3ζ−ζζ3−ζ30000000000
χ644-44-44i−4i4i−4i01-20-112-2-12−2i2i−2i2ii−ii−i-3300−3i3i000000000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ300000000ζ−ζζ3−ζ3−ζζ−ζ3ζ30000000000
χ654-44-4−4i4i−4i4i01-20-112-2-122i−2i2i−2i−ii−ii3-300−3i3i0000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000−ζ3ζ3−ζζ−ζ3ζ3−ζζ0000000000
χ664-44-4−4i4i−4i4i01-20-112-2-122i−2i2i−2i−ii−ii3-300−3i3i000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000ζ3−ζ3ζ−ζζ3−ζ3ζ−ζ0000000000
χ674-44-4−4i4i−4i4i01-20-112-2-122i−2i2i−2i−ii−ii-33003i−3i0000000000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ00000000−ζ3ζ3−ζζζ3−ζ3ζ−ζ0000000000
χ684-44-4−4i4i−4i4i01-20-112-2-122i−2i2i−2i−ii−ii-33003i−3i000000000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ00000000ζ3−ζ3ζ−ζ−ζ3ζ3−ζζ0000000000
χ694-4-444-4-440-21022-1-1-211-1-11-222-2003-3003-3000000002-22-22-22-200000000-11-11-11-11000000000000000000
χ704-4-444-4-440-21022-1-1-211-1-11-222-2003-3003-300000000-22-22-22-22000000001-11-11-11-1000000000000000000
χ714-4-444-4-440-21022-1-1-211-1-11-222-200-3300-33000000002-2-222-2-2200000000-111-1-111-1000000000000000000
χ724-4-444-4-440-21022-1-1-211-1-11-222-200-3300-3300000000-222-2-222-2000000001-1-111-1-11000000000000000000
χ734-4-44-444-40-21022-1-1-21-111-12-2-22003-300-33000000002-2-22-222-200000000-111-11-1-11000000000000000000
χ744-4-44-444-40-21022-1-1-21-111-12-2-22003-300-3300000000-222-22-2-22000000001-1-11-111-1000000000000000000
χ754-4-44-444-40-21022-1-1-21-111-12-2-2200-33003-3000000002-22-2-22-2200000000-11-111-11-1000000000000000000
χ764-4-44-444-40-21022-1-1-21-111-12-2-2200-33003-300000000-22-222-22-2000000001-11-1-11-11000000000000000000
χ7788-8-88i8i−8i−8i02-402-2-44-24−4i−4i4i4i2i2i−2i−2i0000000000000000000000000000000000000000000000000000000000
χ7888-8-88i8i−8i−8i0-420-442-24-22i2i−2i−2i−4i−4i4i4i0000000000000000000000000000000000000000000000000000000000
χ7988-8-8−8i−8i8i8i02-402-2-44-244i4i−4i−4i−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000
χ8088-8-8−8i−8i8i8i0-420-442-24-2−2i−2i2i2i4i4i−4i−4i0000000000000000000000000000000000000000000000000000000000
χ818-88-88i−8i8i−8i0-4204-4-224-22i−2i2i−2i−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ828-88-8−8i8i−8i8i0-4204-4-224-2−2i2i−2i2i4i−4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ838-8-888-8-8802-40-2-2442-4-444-42-2-220000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-802-40-2-2442-44-4-44-222-20000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.