Finite Group Databasebeta

← Group #11790602

Character table — Group #11790602

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111114444444444444444448888888899999999121212121212121212121212121212122424242424242424242424242424242436363636363636363636
order1222444433666666881212121212121212242424242424242422224444222244448888888866661212121224242424242424244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1
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
χ51111111111111111-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ91111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i1111-1-1-1-1ii−i−iii−i−i11-1-1i−iii−i−i
χ101111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-111-1-1-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii-1-111i−i−i−iii
χ111111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-11111-1-1−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-1-111i−i−i−iii
χ121111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iii−i−iii-1-1-1-11111−i−iii−i−iii11-1-1i−iii−i−i
χ131111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−iii−i−iii11-1-1−ii−i−iii
χ141111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-111-1-1-1-111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i-1-111−iiii−i−i
χ151111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-11111-1-1ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-1-111−iiii−i−i
χ161111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−iii−i−i-1-1-1-11111ii−i−iii−i−i11-1-1−ii−i−iii
χ172222222222222222222222222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000-2-20000
χ182222222222222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000220000
χ192222-2-2-2-2222222222i−2i-2-2-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-2-2-22222000000000000000000000000000000000000−2i2i0000
χ202222-2-2-2-222222222−2i2i-2-2-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2-2-222220000000000000000000000000000000000002i−2i0000
χ2122-2-22i−2i2i−2i2222-2-2-2-2002i2i−2i−2i2i2i−2i−2i000000002-22-22i−2i2i−2i0000000000002ζ−2ζ2ζ3−2ζ30000000000002ζ−2ζ2ζ3−2ζ30000000000
χ2222-2-22i−2i2i−2i2222-2-2-2-2002i2i−2i−2i2i2i−2i−2i000000002-22-22i−2i2i−2i000000000000−2ζ2ζ−2ζ32ζ3000000000000−2ζ2ζ−2ζ32ζ30000000000
χ2322-2-22i−2i2i−2i2222-2-2-2-2002i2i−2i−2i2i2i−2i−2i00000000-22-22−2i2i−2i2i002-2002i−2i00000000002-2002i−2i000000000000000000
χ2422-2-22i−2i2i−2i2222-2-2-2-2002i2i−2i−2i2i2i−2i−2i00000000-22-22−2i2i−2i2i00-2200−2i2i0000000000-2200−2i2i000000000000000000
χ2522-2-2−2i2i−2i2i2222-2-2-2-200−2i−2i2i2i−2i−2i2i2i000000002-22-2−2i2i−2i2i0000000000002ζ3−2ζ32ζ−2ζ0000000000002ζ3−2ζ32ζ−2ζ0000000000
χ2622-2-2−2i2i−2i2i2222-2-2-2-200−2i−2i2i2i−2i−2i2i2i000000002-22-2−2i2i−2i2i000000000000−2ζ32ζ3−2ζ2ζ000000000000−2ζ32ζ3−2ζ2ζ0000000000
χ2722-2-2−2i2i−2i2i2222-2-2-2-200−2i−2i2i2i−2i−2i2i2i00000000-22-222i−2i2i−2i002-200−2i2i00000000002-200−2i2i000000000000000000
χ2822-2-2−2i2i−2i2i2222-2-2-2-200−2i−2i2i2i−2i−2i2i2i00000000-22-222i−2i2i−2i00-22002i−2i0000000000-22002i−2i000000000000000000
χ292-22-22i−2i−2i2i22-2-222-2-2002i2i−2i−2i−2i−2i2i2i000000002-2-222i−2i−2i2i2-2002i−2i00000000002-2002i−2i00000000000000000000
χ302-22-22i−2i−2i2i22-2-222-2-2002i2i−2i−2i−2i−2i2i2i000000002-2-222i−2i−2i2i-2200−2i2i0000000000-2200−2i2i00000000000000000000
χ312-22-22i−2i−2i2i22-2-222-2-2002i2i−2i−2i−2i−2i2i2i00000000-222-2−2i2i2i−2i000000002ζ−2ζ2ζ3−2ζ30000000000002ζ−2ζ2ζ3−2ζ300000000000000
χ322-22-22i−2i−2i2i22-2-222-2-2002i2i−2i−2i−2i−2i2i2i00000000-222-2−2i2i2i−2i00000000−2ζ2ζ−2ζ32ζ3000000000000−2ζ2ζ−2ζ32ζ300000000000000
χ332-22-2−2i2i2i−2i22-2-222-2-200−2i−2i2i2i2i2i−2i−2i000000002-2-22−2i2i2i−2i2-200−2i2i00000000002-200−2i2i00000000000000000000
χ342-22-2−2i2i2i−2i22-2-222-2-200−2i−2i2i2i2i2i−2i−2i000000002-2-22−2i2i2i−2i-22002i−2i0000000000-22002i−2i00000000000000000000
χ352-22-2−2i2i2i−2i22-2-222-2-200−2i−2i2i2i2i2i−2i−2i00000000-222-22i−2i−2i2i000000002ζ3−2ζ32ζ−2ζ0000000000002ζ3−2ζ32ζ−2ζ00000000000000
χ362-22-2−2i2i2i−2i22-2-222-2-200−2i−2i2i2i2i2i−2i−2i00000000-222-22i−2i−2i2i00000000−2ζ32ζ3−2ζ2ζ000000000000−2ζ32ζ3−2ζ2ζ00000000000000
χ372-2-2222-2-222-2-2-2-222002222-2-2-2-20000000022-2-222-2-2000000000000000000000000000000000000002i−2i2i−2i
χ382-2-2222-2-222-2-2-2-222002222-2-2-2-20000000022-2-222-2-200000000000000000000000000000000000000−2i2i−2i2i
χ392-2-2222-2-222-2-2-2-222002222-2-2-2-200000000-2-222-2-222000000000000000000000000000000002-22-2000000
χ402-2-2222-2-222-2-2-2-222002222-2-2-2-200000000-2-222-2-22200000000000000000000000000000000-22-22000000
χ412-2-22-2-22222-2-2-2-22200-2-2-2-222220000000022-2-2-2-222000000000000000000000000000000000000002-2-22
χ422-2-22-2-22222-2-2-2-22200-2-2-2-222220000000022-2-2-2-22200000000000000000000000000000000000000-222-2
χ432-2-22-2-22222-2-2-2-22200-2-2-2-2222200000000-2-22222-2-2000000000000000000000000000000002-2-22000000
χ442-2-22-2-22222-2-2-2-22200-2-2-2-2222200000000-2-22222-2-200000000000000000000000000000000-222-2000000
χ45444444441-21-21-21-2441-21-21-21-211-2-211-2-200000000002200220000222200-1-100-1-10000-1-1-1-10000000000
χ46444444441-21-21-21-2441-21-21-21-211-2-211-2-20000000000-2-200-2-20000-2-2-2-200110011000011110000000000
χ47444444441-21-21-21-2-4-41-21-21-21-2-1-122-1-12200000000002200220000-2-2-2-200-1-100-1-1000011110000000000
χ48444444441-21-21-21-2-4-41-21-21-21-2-1-122-1-1220000000000-2-200-2-200002222001100110000-1-1-1-10000000000
χ4944444444-21-21-21-2144-21-21-21-21-2-211-2-211000000002200220022220000-1-100-1-100-1-1-1-100000000000000
χ5044444444-21-21-21-2144-21-21-21-21-2-211-2-21100000000-2-200-2-200-2-2-2-2000011001100111100000000000000
χ5144444444-21-21-21-21-4-4-21-21-21-2122-1-122-1-10000000022002200-2-2-2-20000-1-100-1-100111100000000000000
χ5244444444-21-21-21-21-4-4-21-21-21-2122-1-122-1-100000000-2-200-2-2002222000011001100-1-1-1-100000000000000
χ534444-4-4-4-41-21-21-21-24i−4i-12-12-12-12ii−2i−2i−i−i2i2i00000000002200-2-200002i2i−2i−2i00-1-100110000−i−iii0000000000
χ544444-4-4-4-41-21-21-21-24i−4i-12-12-12-12ii−2i−2i−i−i2i2i0000000000-2-200220000−2i−2i2i2i001100-1-10000ii−i−i0000000000
χ554444-4-4-4-41-21-21-21-2−4i4i-12-12-12-12−i−i2i2iii−2i−2i00000000002200-2-20000−2i−2i2i2i00-1-100110000ii−i−i0000000000
χ564444-4-4-4-41-21-21-21-2−4i4i-12-12-12-12−i−i2i2iii−2i−2i0000000000-2-2002200002i2i−2i−2i001100-1-10000−i−iii0000000000
χ574444-4-4-4-4-21-21-21-214i−4i2-12-12-12-1−2i−2iii2i2i−i−i000000002200-2-2002i2i−2i−2i0000-1-1001100−i−iii00000000000000
χ584444-4-4-4-4-21-21-21-214i−4i2-12-12-12-1−2i−2iii2i2i−i−i00000000-2-2002200−2i−2i2i2i00001100-1-100ii−i−i00000000000000
χ594444-4-4-4-4-21-21-21-21−4i4i2-12-12-12-12i2i−i−i−2i−2iii000000002200-2-200−2i−2i2i2i0000-1-1001100ii−i−i00000000000000
χ604444-4-4-4-4-21-21-21-21−4i4i2-12-12-12-12i2i−i−i−2i−2iii00000000-2-20022002i2i−2i−2i00001100-1-100−i−iii00000000000000
χ6144-4-44i−4i4i−4i1-21-2-12-1200i−2i−i2ii−2i−i2i3ζ−3ζ003ζ3−3ζ30000000000002-2002i−2i00002ζ−2ζ2ζ3−2ζ300-1100−ii0000−ζζ−ζ3ζ30000000000
χ6244-4-44i−4i4i−4i1-21-2-12-1200i−2i−i2ii−2i−i2i3ζ−3ζ003ζ3−3ζ3000000000000-2200−2i2i0000−2ζ2ζ−2ζ32ζ3001-100i−i0000ζ−ζζ3−ζ30000000000
χ6344-4-44i−4i4i−4i1-21-2-12-1200i−2i−i2ii−2i−i2i−3ζ3ζ00−3ζ33ζ30000000000002-2002i−2i0000−2ζ2ζ−2ζ32ζ300-1100−ii0000ζ−ζζ3−ζ30000000000
χ6444-4-44i−4i4i−4i1-21-2-12-1200i−2i−i2ii−2i−i2i−3ζ3ζ00−3ζ33ζ3000000000000-2200−2i2i00002ζ−2ζ2ζ3−2ζ3001-100i−i0000−ζζ−ζ3ζ30000000000
χ6544-4-4−4i4i−4i4i1-21-2-12-1200−i2ii−2i−i2ii−2i3ζ3−3ζ3003ζ−3ζ0000000000002-200−2i2i00002ζ3−2ζ32ζ−2ζ00-1100i−i0000−ζ3ζ3−ζζ0000000000
χ6644-4-4−4i4i−4i4i1-21-2-12-1200−i2ii−2i−i2ii−2i3ζ3−3ζ3003ζ−3ζ000000000000-22002i−2i0000−2ζ32ζ3−2ζ2ζ001-100−ii0000ζ3−ζ3ζ−ζ0000000000
χ6744-4-4−4i4i−4i4i1-21-2-12-1200−i2ii−2i−i2ii−2i−3ζ33ζ300−3ζ3ζ0000000000002-200−2i2i0000−2ζ32ζ3−2ζ2ζ00-1100i−i0000ζ3−ζ3ζ−ζ0000000000
χ6844-4-4−4i4i−4i4i1-21-2-12-1200−i2ii−2i−i2ii−2i−3ζ33ζ300−3ζ3ζ000000000000-22002i−2i00002ζ3−2ζ32ζ−2ζ001-100−ii0000−ζ3ζ3−ζζ0000000000
χ694-44-44i−4i−4i4i-212-1-212-100−2ii2i−i2i−i−2ii003ζ−3ζ003ζ3−3ζ3000000002-2002i−2i002ζ−2ζ2ζ3−2ζ30000-1100−ii00−ζζ−ζ3ζ300000000000000
χ704-44-44i−4i−4i4i-212-1-212-100−2ii2i−i2i−i−2ii003ζ−3ζ003ζ3−3ζ300000000-2200−2i2i00−2ζ2ζ−2ζ32ζ300001-100i−i00ζ−ζζ3−ζ300000000000000
χ714-44-44i−4i−4i4i-212-1-212-100−2ii2i−i2i−i−2ii00−3ζ3ζ00−3ζ33ζ3000000002-2002i−2i00−2ζ2ζ−2ζ32ζ30000-1100−ii00ζ−ζζ3−ζ300000000000000
χ724-44-44i−4i−4i4i-212-1-212-100−2ii2i−i2i−i−2ii00−3ζ3ζ00−3ζ33ζ300000000-2200−2i2i002ζ−2ζ2ζ3−2ζ300001-100i−i00−ζζ−ζ3ζ300000000000000
χ734-44-4−4i4i4i−4i-212-1-212-1002i−i−2ii−2ii2i−i003ζ3−3ζ3003ζ−3ζ000000002-200−2i2i002ζ3−2ζ32ζ−2ζ0000-1100i−i00−ζ3ζ3−ζζ00000000000000
χ744-44-4−4i4i4i−4i-212-1-212-1002i−i−2ii−2ii2i−i003ζ3−3ζ3003ζ−3ζ00000000-22002i−2i00−2ζ32ζ3−2ζ2ζ00001-100−ii00ζ3−ζ3ζ−ζ00000000000000
χ754-44-4−4i4i4i−4i-212-1-212-1002i−i−2ii−2ii2i−i00−3ζ33ζ300−3ζ3ζ000000002-200−2i2i00−2ζ32ζ3−2ζ2ζ0000-1100i−i00ζ3−ζ3ζ−ζ00000000000000
χ764-44-4−4i4i4i−4i-212-1-212-1002i−i−2ii−2ii2i−i00−3ζ33ζ300−3ζ3ζ00000000-22002i−2i002ζ3−2ζ32ζ−2ζ00001-100−ii00−ζ3ζ3−ζζ00000000000000
χ7788-8-88i−8i8i−8i-42-424-24-200−4i2i4i−2i−4i2i4i−2i0000000000000000000000000000000000000000000000000000000000
χ7888-8-8−8i8i−8i8i-42-424-24-2004i−2i−4i2i4i−2i−4i2i0000000000000000000000000000000000000000000000000000000000
χ798-88-88i−8i−8i8i2-4-242-4-24002i−4i−2i4i−2i4i2i−4i0000000000000000000000000000000000000000000000000000000000
χ808-88-8−8i8i8i−8i2-4-242-4-2400−2i4i2i−4i2i−4i−2i4i0000000000000000000000000000000000000000000000000000000000
χ818-8-8888-8-82-4-24-242-4002-42-4-24-240000000000000000000000000000000000000000000000000000000000
χ828-8-8888-8-8-424-24-2-4200-42-424-24-20000000000000000000000000000000000000000000000000000000000
χ838-8-88-8-8882-4-24-242-400-24-242-42-40000000000000000000000000000000000000000000000000000000000
χ848-8-88-8-888-424-24-2-42004-24-2-42-420000000000000000000000000000000000000000000000000000000000

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