Finite Group Databasebeta

← Group #11785987

Character table — Group #11785987

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111114444444444444444448888888899999999121212121212121212121212121212122424242424242424242424242424242436363636363636363636
order12224444334466666612121212121212121212121212121212222244448888888888888888242424242424242424242424242424244444444444
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
χ51111111111-1-111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ61111111111-1-111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ81111111111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1
χ91111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-111-1-111-1-1
χ101111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii1-1-1-111-1-111
χ111111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i1-1-1-111-1-111
χ121111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-111-1-111-1-1
χ131111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii-1111-1-1-1-111
χ141111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i-11-1-11111-1-1
χ151111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii-11-1-11111-1-1
χ161111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i-1111-1-1-1-111
χ172222222222222222222222222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000-2-200000000
χ182222222222-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000002200000000
χ192222-2-2-2-2222-2222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000-2200000000
χ202222-2-2-2-222-22222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000002-200000000
χ2122-2-222-2-2220022-2-2-2-222-2-222-2-20000000022-2-222-2-2000000000000000000000000000000000000002i−2i2i−2i
χ2222-2-222-2-2220022-2-2-2-222-2-222-2-20000000022-2-222-2-200000000000000000000000000000000000000−2i2i−2i2i
χ2322-2-222-2-2220022-2-2-2-222-2-222-2-200000000-2-222-2-22200000000000000000000000000000000002i−2i2i−2i0000
χ2422-2-222-2-2220022-2-2-2-222-2-222-2-200000000-2-222-2-2220000000000000000000000000000000000−2i2i−2i2i0000
χ2522-2-2-2-222220022-2-2-2-2-2-222-2-2220000000022-2-2-2-222000000000000000000000000000000000000002i−2i−2i2i
χ2622-2-2-2-222220022-2-2-2-2-2-222-2-2220000000022-2-2-2-22200000000000000000000000000000000000000−2i2i2i−2i
χ2722-2-2-2-222220022-2-2-2-2-2-222-2-22200000000-2-22222-2-200000000000000000000000000000000002i−2i−2i2i0000
χ2822-2-2-2-222220022-2-2-2-2-2-222-2-22200000000-2-22222-2-20000000000000000000000000000000000−2i2i2i−2i0000
χ292-22-22i−2i2i−2i2200-2-222-2-22i−2i2i−2i2i−2i2i−2i000000002-22-22i−2i2i−2i0000000000002ζ−2ζ2ζ3−2ζ30000000000002ζ−2ζ2ζ3−2ζ30000000000
χ302-22-22i−2i2i−2i2200-2-222-2-22i−2i2i−2i2i−2i2i−2i000000002-22-22i−2i2i−2i000000000000−2ζ2ζ−2ζ32ζ3000000000000−2ζ2ζ−2ζ32ζ30000000000
χ312-22-22i−2i2i−2i2200-2-222-2-22i−2i2i−2i2i−2i2i−2i00000000-22-22−2i2i−2i2i000000002ζ−2ζ2ζ3−2ζ30000000000002ζ−2ζ2ζ3−2ζ300000000000000
χ322-22-22i−2i2i−2i2200-2-222-2-22i−2i2i−2i2i−2i2i−2i00000000-22-22−2i2i−2i2i00000000−2ζ2ζ−2ζ32ζ3000000000000−2ζ2ζ−2ζ32ζ300000000000000
χ332-22-2−2i2i−2i2i2200-2-222-2-2−2i2i−2i2i−2i2i−2i2i000000002-22-2−2i2i−2i2i0000000000002ζ3−2ζ32ζ−2ζ0000000000002ζ3−2ζ32ζ−2ζ0000000000
χ342-22-2−2i2i−2i2i2200-2-222-2-2−2i2i−2i2i−2i2i−2i2i000000002-22-2−2i2i−2i2i000000000000−2ζ32ζ3−2ζ2ζ000000000000−2ζ32ζ3−2ζ2ζ0000000000
χ352-22-2−2i2i−2i2i2200-2-222-2-2−2i2i−2i2i−2i2i−2i2i00000000-22-222i−2i2i−2i000000002ζ3−2ζ32ζ−2ζ0000000000002ζ3−2ζ32ζ−2ζ00000000000000
χ362-22-2−2i2i−2i2i2200-2-222-2-2−2i2i−2i2i−2i2i−2i2i00000000-22-222i−2i2i−2i00000000−2ζ32ζ3−2ζ2ζ000000000000−2ζ32ζ3−2ζ2ζ00000000000000
χ372-2-222i−2i−2i2i2200-2-2-2-2222i−2i−2i2i2i−2i−2i2i000000002-2-222i−2i−2i2i2ζ−2ζ2ζ3−2ζ30000000000002ζ−2ζ2ζ3−2ζ30000000000000000000000
χ382-2-222i−2i−2i2i2200-2-2-2-2222i−2i−2i2i2i−2i−2i2i000000002-2-222i−2i−2i2i−2ζ2ζ−2ζ32ζ3000000000000−2ζ2ζ−2ζ32ζ30000000000000000000000
χ392-2-222i−2i−2i2i2200-2-2-2-2222i−2i−2i2i2i−2i−2i2i00000000-222-2−2i2i2i−2i00002ζ3−2ζ32ζ−2ζ0000000000002ζ3−2ζ32ζ−2ζ000000000000000000
χ402-2-222i−2i−2i2i2200-2-2-2-2222i−2i−2i2i2i−2i−2i2i00000000-222-2−2i2i2i−2i0000−2ζ32ζ3−2ζ2ζ000000000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ412-2-22−2i2i2i−2i2200-2-2-2-222−2i2i2i−2i−2i2i2i−2i000000002-2-22−2i2i2i−2i2ζ3−2ζ32ζ−2ζ0000000000002ζ3−2ζ32ζ−2ζ0000000000000000000000
χ422-2-22−2i2i2i−2i2200-2-2-2-222−2i2i2i−2i−2i2i2i−2i000000002-2-22−2i2i2i−2i−2ζ32ζ3−2ζ2ζ000000000000−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ432-2-22−2i2i2i−2i2200-2-2-2-222−2i2i2i−2i−2i2i2i−2i00000000-222-22i−2i−2i2i00002ζ−2ζ2ζ3−2ζ30000000000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ442-2-22−2i2i2i−2i2200-2-2-2-222−2i2i2i−2i−2i2i2i−2i00000000-222-22i−2i−2i2i0000−2ζ2ζ−2ζ32ζ3000000000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ45444444441-2441-21-21-211-2-2-2-21111-2-211-2-200000000000000002222222200000000-1-1-1-1-1-1-1-10000000000
χ46444444441-2441-21-21-211-2-2-2-21111-2-211-2-20000000000000000-2-2-2-2-2-2-2-200000000111111110000000000
χ47444444441-2-4-41-21-21-211-2-2-2-211-1-122-1-12200000000000000002222-2-2-2-200000000-1-1-1-111110000000000
χ48444444441-2-4-41-21-21-211-2-2-2-211-1-122-1-1220000000000000000-2-2-2-22222000000001111-1-1-1-10000000000
χ4944444444-2144-21-21-21-2-21111-2-2-2-211-2-211000000002222222200000000-1-1-1-1-1-1-1-1000000000000000000
χ5044444444-2144-21-21-21-2-21111-2-2-2-211-2-21100000000-2-2-2-2-2-2-2-20000000011111111000000000000000000
χ5144444444-21-4-4-21-21-21-2-21111-2-222-1-122-1-1000000002222-2-2-2-200000000-1-1-1-11111000000000000000000
χ5244444444-21-4-4-21-21-21-2-21111-2-222-1-122-1-100000000-2-2-2-22222000000001111-1-1-1-1000000000000000000
χ534444-4-4-4-41-24-41-21-21-2-1-12222-1-111-2-2-1-12200000000000000002i2i−2i−2i2i2i−2i−2i00000000−i−iii−i−iii0000000000
χ544444-4-4-4-41-24-41-21-21-2-1-12222-1-111-2-2-1-1220000000000000000−2i−2i2i2i−2i−2i2i2i00000000ii−i−iii−i−i0000000000
χ554444-4-4-4-41-2-441-21-21-2-1-12222-1-1-1-12211-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000−i−iiiii−i−i0000000000
χ564444-4-4-4-41-2-441-21-21-2-1-12222-1-1-1-12211-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000ii−i−i−i−iii0000000000
χ574444-4-4-4-4-214-4-21-21-2122-1-1-1-122-2-21122-1-1000000002i2i−2i−2i2i2i−2i−2i00000000−i−iii−i−iii000000000000000000
χ584444-4-4-4-4-214-4-21-21-2122-1-1-1-122-2-21122-1-100000000−2i−2i2i2i−2i−2i2i2i00000000ii−i−iii−i−i000000000000000000
χ594444-4-4-4-4-21-44-21-21-2122-1-1-1-12222-1-1-2-211000000002i2i−2i−2i−2i−2i2i2i00000000−i−iiiii−i−i000000000000000000
χ604444-4-4-4-4-21-44-21-21-2122-1-1-1-12222-1-1-2-21100000000−2i−2i2i2i2i2i−2i−2i00000000ii−i−i−i−iii000000000000000000
χ614-44-44i−4i4i−4i1-200-121-2-12i−i−2i2i−2i2ii−i3-3003i−3i0000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000−ζζ−ζ3ζ3−ζζ−ζ3ζ30000000000
χ624-44-44i−4i4i−4i1-200-121-2-12i−i−2i2i−2i2ii−i3-3003i−3i000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000ζ−ζζ3−ζ3ζ−ζζ3−ζ30000000000
χ634-44-44i−4i4i−4i1-200-121-2-12i−i−2i2i−2i2ii−i-3300−3i3i0000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ300000000−ζζ−ζ3ζ3ζ−ζζ3−ζ30000000000
χ644-44-44i−4i4i−4i1-200-121-2-12i−i−2i2i−2i2ii−i-3300−3i3i000000000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ300000000ζ−ζζ3−ζ3−ζζ−ζ3ζ30000000000
χ654-44-4−4i4i−4i4i1-200-121-2-12−ii2i−2i2i−2i−ii3-300−3i3i0000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00000000−ζ3ζ3−ζζ−ζ3ζ3−ζζ0000000000
χ664-44-4−4i4i−4i4i1-200-121-2-12−ii2i−2i2i−2i−ii3-300−3i3i000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00000000ζ3−ζ3ζ−ζζ3−ζ3ζ−ζ0000000000
χ674-44-4−4i4i−4i4i1-200-121-2-12−ii2i−2i2i−2i−ii-33003i−3i0000000000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ00000000−ζ3ζ3−ζζζ3−ζ3ζ−ζ0000000000
χ684-44-4−4i4i−4i4i1-200-121-2-12−ii2i−2i2i−2i−ii-33003i−3i000000000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ00000000ζ3−ζ3ζ−ζ−ζ3ζ3−ζζ0000000000
χ694-4-444i−4i−4i4i-21002-12-1-21−2i2i−iii−i2i−2i003i−3i003-3000000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ00000000−ζζ−ζ3ζ3−ζ3ζ3−ζζ000000000000000000
χ704-4-444i−4i−4i4i-21002-12-1-21−2i2i−iii−i2i−2i003i−3i003-300000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ00000000ζ−ζζ3−ζ3ζ3−ζ3ζ−ζ000000000000000000
χ714-4-444i−4i−4i4i-21002-12-1-21−2i2i−iii−i2i−2i00−3i3i00-33000000002ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ00000000−ζζ−ζ3ζ3ζ3−ζ3ζ−ζ000000000000000000
χ724-4-444i−4i−4i4i-21002-12-1-21−2i2i−iii−i2i−2i00−3i3i00-3300000000−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ00000000ζ−ζζ3−ζ3−ζ3ζ3−ζζ000000000000000000
χ734-4-44−4i4i4i−4i-21002-12-1-212i−2ii−i−ii−2i2i003i−3i00-33000000002ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ300000000−ζ3ζ3−ζζζ−ζζ3−ζ3000000000000000000
χ744-4-44−4i4i4i−4i-21002-12-1-212i−2ii−i−ii−2i2i003i−3i00-3300000000−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ300000000ζ3−ζ3ζ−ζ−ζζ−ζ3ζ3000000000000000000
χ754-4-44−4i4i4i−4i-21002-12-1-212i−2ii−i−ii−2i2i00−3i3i003-3000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ300000000−ζ3ζ3−ζζ−ζζ−ζ3ζ3000000000000000000
χ764-4-44−4i4i4i−4i-21002-12-1-212i−2ii−i−ii−2i2i00−3i3i003-300000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ300000000ζ3−ζ3ζ−ζζ−ζζ3−ζ3000000000000000000
χ7788-8-888-8-82-4002-4-24-242244-4-4-2-20000000000000000000000000000000000000000000000000000000000
χ7888-8-888-8-8-4200-424-24-2-4-4-2-222440000000000000000000000000000000000000000000000000000000000
χ7988-8-8-8-8882-4002-4-24-24-2-2-4-444220000000000000000000000000000000000000000000000000000000000
χ8088-8-8-8-888-4200-424-24-24422-2-2-4-40000000000000000000000000000000000000000000000000000000000
χ818-88-88i−8i8i−8i-42004-2-424-2−4i4i2i−2i2i−2i−4i4i0000000000000000000000000000000000000000000000000000000000
χ828-88-8−8i8i−8i8i-42004-2-424-24i−4i−2i2i−2i2i4i−4i0000000000000000000000000000000000000000000000000000000000
χ838-8-888i−8i−8i8i2-400-24-242-42i−2i4i−4i−4i4i−2i2i0000000000000000000000000000000000000000000000000000000000
χ848-8-88−8i8i8i−8i2-400-24-242-4−2i2i−4i4i4i−4i2i−2i0000000000000000000000000000000000000000000000000000000000

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