Finite Group Databasebeta

← Group #11921113

Character table — Group #11921113

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222224444444466668888888888881212121212121212121216161616161616161616161616161616161636363636727272727272
order124423461212246661212122244333666121212121212246666121212126666666661212121212121212128888444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111-1-11-1-11-1-11111111111111111-1-111-1-111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1
χ41111111111-1-11-1-11-1-11111111111111111-1-111-1-111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-1-1111-1-11-1-1111-1-11-11-1111111-1-1-1-1-1-1-111-1-1-11-111-1-1-1111111111-1-1-1-1-1-1ii−i−ii−ii−ii−i
χ611-1-1-1111-1-11-1-1111-1-11-11-1111111-1-1-1-1-1-1-111-1-1-11-111-1-1-1111111111-1-1-1-1-1-1−i−iii−ii−ii−ii
χ711-1-1-1111-1-1-11-1-1-11111-11-1111111-1-1-1-1-1-11-11-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111ii−i−ii−i−ii−ii
χ811-1-1-1111-1-1-11-1-1-11111-11-1111111-1-1-1-1-1-11-11-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111−i−iii−iii−ii−i
χ92222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ102222222222-2-22-2-22-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2-1-1-1111111-1-1-11111110000000000
χ1122222-12-1-1-122-1-1-1-1-1-122222-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-12-1-122-1-1-1-12-1-122-1-1-1-10000000000
χ1222222-12-1-1-122-1-1-1-1-1-12222-12-1-12-1-1-122-1-122-1-1-1-1-1-1-1-1-12-1-1-122-1-1-12-1-1-122-1-10000000000
χ1322222-12-1-1-122-1-1-1-1-1-12222-1-12-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-12-1-1-1-1220000000000
χ1422222-12-1-1-1-2-2-111-11122222-1-12-1-122-1-1-1-1-2-2-1-111-1-1112-1-1-2-211112-1-1-2-211110000000000
χ1522222-12-1-1-1-2-2-111-1112222-12-1-12-1-1-122-1-1-2-2-1-111-1-111-12-111-2-211-12-111-2-2110000000000
χ1622222-12-1-1-1-2-2-111-1112222-1-12-1-12-1-1-1-122-2-2-1-111-1-111-1-121111-2-2-1-121111-2-20000000000
χ172222-22-222200-200-200-222-222222222222200-22002-200-2-2-2000000-2-2-20000000000000000
χ182222-22-222200-200-200-222-2-1-1-1-1-1-1-1-1-1-1-1-100-22002-200111−i3i3−i3i3−i3i3111−i3i3−i3i3−i3i30000000000
χ192222-22-222200-200-200-222-2-1-1-1-1-1-1-1-1-1-1-1-100-22002-200111i3−i3i3−i3i3−i3111i3−i3i3−i3i3−i30000000000
χ202222-2-1-2-1-1-1001−i3i31−i3i3-222-22-1-12-1-122-1-1-1-1001-1−i3i3-11−i3i3-21100−i3i3i3−i3-21100−i3i3i3−i30000000000
χ212222-2-1-2-1-1-1001−i3i31−i3i3-222-2-12-1-12-1-1-122-1-1001-1−i3i3-11−i3i31-21i3−i300−i3i31-21i3−i300−i3i30000000000
χ222222-2-1-2-1-1-1001−i3i31−i3i3-222-2-1-12-1-12-1-1-1-122001-1−i3i3-11−i3i311-2−i3i3i3−i30011-2−i3i3i3−i3000000000000
χ232222-2-1-2-1-1-1001i3−i31i3−i3-222-22-1-12-1-122-1-1-1-1001-1i3−i3-11i3−i3-21100i3−i3−i3i3-21100i3−i3−i3i30000000000
χ242222-2-1-2-1-1-1001i3−i31i3−i3-222-2-12-1-12-1-1-122-1-1001-1i3−i3-11i3−i31-21−i3i300i3−i31-21−i3i300i3−i30000000000
χ252222-2-1-2-1-1-1001i3−i31i3−i3-222-2-1-12-1-12-1-1-1-122001-1i3−i3-11i3−i311-2i3−i3−i3i30011-2i3−i3−i3i3000000000000
χ2622-2-222-22-2-200200-200-2-222222222-2-2-2-2-2-200-2-2002200222000000-2-2-20000000000000000
χ2722-2-222-22-2-200200-200-2-222-1-1-1-1-1-111111100-2-2002200-1-1-1−i3i3−i3i3−i3i3111i3−i3i3−i3i3−i30000000000
χ2822-2-222-22-2-200200-200-2-222-1-1-1-1-1-111111100-2-2002200-1-1-1i3−i3i3−i3i3−i3111−i3i3−i3i3−i3i30000000000
χ2922-2-22-1-2-11100-1−i3i31i3−i3-2-2222-1-12-1-1-2-211110011i3−i3-1-1−i3i32-1-100−i3i3i3−i3-21100i3−i3−i3i30000000000
χ3022-2-22-1-2-11100-1−i3i31i3−i3-2-222-12-1-12-111-2-2110011i3−i3-1-1−i3i3-12-1i3−i300−i3i31-21−i3i300i3−i30000000000
χ3122-2-22-1-2-11100-1−i3i31i3−i3-2-222-1-12-1-121111-2-20011i3−i3-1-1−i3i3-1-12−i3i3i3−i30011-2i3−i3−i3i3000000000000
χ3222-2-22-1-2-11100-1i3−i31−i3i3-2-2222-1-12-1-1-2-211110011−i3i3-1-1i3−i32-1-100i3−i3−i3i3-21100−i3i3i3−i30000000000
χ3322-2-22-1-2-11100-1i3−i31−i3i3-2-222-12-1-12-111-2-2110011−i3i3-1-1i3−i3-12-1−i3i300i3−i31-21i3−i300−i3i30000000000
χ3422-2-22-1-2-11100-1i3−i31−i3i3-2-222-1-12-1-121111-2-20011−i3i3-1-1i3−i3-1-12i3−i3−i3i30011-2−i3i3i3−i3000000000000
χ3522-2-2-2222-2-22-2-2222-2-22-22-2-1-1-1-1-1-1111111-222-2-2-22-222111-1-1-1-1-1-1-1-1-11111110000000000
χ3622-2-2-2222-2-2-22-2-2-22222-22-2-1-1-1-1-1-11111112-22-2222-2-2-2111111111-1-1-1-1-1-1-1-1-10000000000
χ3722-2-2-2-12-1112-21-1-1-1112-22-22-1-12-1-1-2-21111-22-1111-11-1-1-21122-1-1-1-12-1-1-2-211110000000000
χ3822-2-2-2-12-1112-21-1-1-1112-22-2-12-1-12-111-2-211-22-1111-11-1-11-21-1-122-1-1-12-111-2-2110000000000
χ3922-2-2-2-12-1112-21-1-1-1112-22-2-1-12-1-121111-2-2-22-1111-11-1-111-2-1-1-1-122-1-121111-2-20000000000
χ4022-2-2-2-12-111-22111-1-1-12-22-22-1-12-1-1-2-211112-2-11-1-1-1111-211-2-211112-1-122-1-1-1-10000000000
χ4122-2-2-2-12-111-22111-1-1-12-22-2-12-1-12-111-2-2112-2-11-1-1-11111-2111-2-211-12-1-1-122-1-10000000000
χ4222-2-2-2-12-111-22111-1-1-12-22-2-1-12-1-121111-2-22-2-11-1-1-111111-21111-2-2-1-12-1-1-1-1220000000000
χ43333333333333333333-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-10000000000000000001111-1-111-1-1
χ44333333333333333333-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1000000000000000000-1-1-1-111-1-111
χ453333333333-3-33-3-33-3-3-1-1-1-100000000000011-1-111-1-1110000000000000000001111-1-1-1-111
χ463333333333-3-33-3-33-3-3-1-1-1-100000000000011-1-111-1-111000000000000000000-1-1-1-11111-1-1
χ4733-3-3-3333-3-33-3-3333-3-3-11-110000000000001-1-1111-11-1-1000000000000000000ii−i−i−iii−i−ii
χ4833-3-3-3333-3-33-3-3333-3-3-11-110000000000001-1-1111-11-1-1000000000000000000−i−iiii−i−iii−i
χ4933-3-3-3333-3-3-33-3-3-3333-11-11000000000000-11-11-1-1-1111000000000000000000ii−i−i−ii−iii−i
χ5033-3-3-3333-3-3-33-3-3-3333-11-11000000000000-11-11-1-1-1111000000000000000000−i−iiii−ii−i−ii
χ514-44i−4i040-44i−4i000000000000-2-2-22222i−2i2i−2i2i−2i00000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ524-44i−4i040-44i−4i000000000000-2-2-22222i−2i2i−2i2i−2i0000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ534-4−4i4i040-4−4i4i000000000000-2-2-2222−2i2i−2i2i−2i2i0000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ544-4−4i4i040-4−4i4i000000000000-2-2-2222−2i2i−2i2i−2i2i00000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ5566666-36-3-3-366-3-3-3-3-3-3-2-2-2-2000000000000-2-2111111110000000000000000000000000000
χ5666666-36-3-3-3-6-6-333-333-2-2-2-20000000000002211-1-111-1-10000000000000000000000000000
χ576666-66-666600-600-6002-2-22000000000000002-200-22000000000000000000000000000000
χ586666-6-3-6-3-3-3003−3i33i33−3i33i32-2-2200000000000000-11i3−i31-1i3−i30000000000000000000000000000
χ596666-6-3-6-3-3-30033i3−3i333i3−3i32-2-2200000000000000-11−i3i31-1−i3i30000000000000000000000000000
χ6066-6-666-66-6-600600-60022-2-2000000000000002200-2-2000000000000000000000000000000
χ6166-6-66-3-6-33300-3−3i33i333i3−3i322-2-200000000000000-1-1−i3i311i3−i30000000000000000000000000000
χ6266-6-66-3-6-33300-33i3−3i33−3i33i322-2-200000000000000-1-1i3−i311−i3i30000000000000000000000000000
χ6366-6-6-6-36-3336-63-3-3-333-22-220000000000002-21-1-1-11-1110000000000000000000000000000
χ6466-6-6-6-36-333-66333-3-3-3-22-22000000000000-221-1111-1-1-10000000000000000000000000000
χ658-88i−8i080-88i−8i000000000000222-2-2-2−2i2i−2i2i−2i2i00000000000000000000000000000000000000
χ668-88i−8i0-404−4i4i00000000000022-4-2-24−2i2i−2i2i4i−4i00000000000000000000000000000000000000
χ678-88i−8i0-404−4i4i0000000000002-42-24-2−2i2i4i−4i−2i2i00000000000000000000000000000000000000
χ688-88i−8i0-404−4i4i000000000000-4224-2-24i−4i−2i2i−2i2i00000000000000000000000000000000000000
χ698-8−8i8i080-8−8i8i000000000000222-2-2-22i−2i2i−2i2i−2i00000000000000000000000000000000000000
χ708-8−8i8i0-4044i−4i00000000000022-4-2-242i−2i2i−2i−4i4i00000000000000000000000000000000000000
χ718-8−8i8i0-4044i−4i0000000000002-42-24-22i−2i−4i4i2i−2i00000000000000000000000000000000000000
χ728-8−8i8i0-4044i−4i000000000000-4224-2-2−4i4i2i−2i2i−2i00000000000000000000000000000000000000

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