Finite Group Databasebeta

← Group #72319287

Character table — Group #72319287

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85
size11112222222244444444488888888888888888888888888816161616161616161616161616161616161616161616161616161632323232323232323232
order12224444444424444888822244444444888888888888161616164488888888888888816161616161616161616244488881616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1-1-111-1-1
χ41111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ51111111111111111111111-1-11-1-111111111111111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1
χ61111111111111111111111-1-11-1-111111111-1-1-1-1111111111-1-1111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ71111111111111111111111-1-11-1-11-1-1-1-11111111-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111
χ81111111111111111111111-1-11-1-11-1-1-1-1111-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1-1-11111111111-1-1-1-11-1-1111-1-1-1-1
χ911111111111111-1-111111-111-111-111111-1-1111111111111111-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ1011111111111111-1-111111-111-111-111111-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-1-11-1-11111
χ1111111111111111-1-111111-111-111-1-1-1-1-11-1-11111-1-1-1-11111111-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-111
χ1211111111111111-1-111111-111-111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-111-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ1311111111111111-1-111111-1-1-1-1-1-1-111111-1-1111111111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-111-111-1-111
χ1411111111111111-1-111111-1-1-1-1-1-1-111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1
χ1511111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11-1-1-1-1-1-1-111-1-1-1-111111111-1-1111111111111-1-1-1-1-1-1
χ1611111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-111-1-1-11111
χ171111111-1-11-1-1-1111-111-1-1-1111-1-1-1ii−i−i-1-1-1ii−i−iii−i−i1ii−i−i-111i−i11-1-1i−ii−iii−i−ii−iii−i−i11-1-11-11-1i−ii−i1-1
χ181111111-1-11-1-1-1111-111-1-1-1111-1-1-1ii−i−i-1-1-1−i−iiiii−i−i1−i−iii-111i−i-1-111i−i−iiii−i−i−ii−i−iii-1-111-1-111i−i−ii-11
χ191111111-1-11-1-1-1111-111-1-1-1111-1-1-1−i−iii-1-1-1ii−i−i−i−iii1ii−i−i-111−ii-1-111−iii−i−i−iiii−iii−i−i-1-111-1-111−iii−i-11
χ201111111-1-11-1-1-1111-111-1-1-1111-1-1-1−i−iii-1-1-1−i−iii−i−iii1−i−iii-111−ii11-1-1−ii−ii−i−iii−ii−i−iii11-1-11-11-1−ii−ii1-1
χ211111111-1-11-1-1-1111-111-1-1-1-1-1111-1ii−i−i-1-1-1ii−i−iii−i−i1−i−iii1-11i−i11-1-1i−ii−i−i−iii−ii−i−iii-1-11111-1-1−iii−i-11
χ221111111-1-11-1-1-1111-111-1-1-1-1-1111-1ii−i−i-1-1-1−i−iiiii−i−i1ii−i−i1-11i−i-1-111i−i−ii−i−iiii−iii−i−i11-1-1-11-11−ii−ii1-1
χ231111111-1-11-1-1-1111-111-1-1-1-1-1111-1−i−iii-1-1-1ii−i−i−i−iii1−i−iii1-11−ii-1-111−iii−iii−i−i−ii−i−iii11-1-1-11-11i−ii−i1-1
χ241111111-1-11-1-1-1111-111-1-1-1-1-1111-1−i−iii-1-1-1−i−iii−i−iii1ii−i−i1-11−ii11-1-1−ii−iiii−i−ii−iii−i−i-1-11111-1-1i−i−ii-11
χ251111111-1-11-1-1-11-1-1-111-1-1111-1-1-11ii−i−i-111ii−i−iii−i−i1ii−i−i-11-1−ii11-1-1−iii−iii−i−ii−i−i−iii11-1-1-11-11−ii−ii-11
χ261111111-1-11-1-1-11-1-1-111-1-1111-1-1-11ii−i−i-111−i−iiiii−i−i1−i−iii-11-1−ii-1-111−ii−iiii−i−i−iiii−i−i-1-11111-1-1−iii−i1-1
χ271111111-1-11-1-1-11-1-1-111-1-1111-1-1-11−i−iii-111ii−i−i−i−iii1ii−i−i-11-1i−i-1-111i−ii−i−i−iiii−i−i−iii-1-11111-1-1i−i−ii1-1
χ281111111-1-11-1-1-11-1-1-111-1-1111-1-1-11−i−iii-111−i−iii−i−iii1−i−iii-11-1i−i11-1-1i−i−ii−i−iii−iiii−i−i11-1-1-11-11i−ii−i-11
χ291111111-1-11-1-1-11-1-1-111-1-11-1-1-1111ii−i−i-111ii−i−iii−i−i1−i−iii1-1-1−ii11-1-1−iii−i−i−iii−iiii−i−i-1-111-1-111i−i−ii1-1
χ301111111-1-11-1-1-11-1-1-111-1-11-1-1-1111ii−i−i-111−i−iiiii−i−i1ii−i−i1-1-1−ii-1-111−ii−ii−i−iiii−i−i−iii11-1-11-11-1i−ii−i-11
χ311111111-1-11-1-1-11-1-1-111-1-11-1-1-1111−i−iii-111ii−i−i−i−iii1−i−iii1-1-1i−i-1-111i−ii−iii−i−i−iiii−i−i11-1-11-11-1−ii−ii-11
χ321111111-1-11-1-1-11-1-1-111-1-11-1-1-1111−i−iii-111−i−iii−i−iii1ii−i−i1-1-1i−i11-1-1i−i−iiii−i−ii−i−i−iii-1-111-1-111−iii−i1-1
χ3322222222222222222-2-2-2-220020022222-2-2-20000-2-2-2-2-2000000-2-2-200002200000000000000000000000000
χ3422222222222222222-2-2-2-22002002-2-2-2-2-2-2-200002222-2000000-2220000-2-200000000000000000000000000
χ3522222222222222-2-22-2-2-2-2-200-200-22222-2220000-2-2-2-2-20000002220000-2-200000000000000000000000000
χ3622222222222222-2-22-2-2-2-2-200-200-2-2-2-2-2-22200002222-20000002-2-200002200000000000000000000000000
χ372222222-2-22-2-2-2222-2-2-222-200200-22i2i−2i−2i2220000−2i−2i2i2i-2000000-2−2i2i00002i−2i00000000000000000000000000
χ382222222-2-22-2-2-2222-2-2-222-200200-2−2i−2i2i2i22200002i2i−2i−2i-2000000-22i−2i0000−2i2i00000000000000000000000000
χ392222222-2-22-2-2-22-2-2-2-2-222200-20022i2i−2i−2i2-2-20000−2i−2i2i2i-200000022i−2i0000−2i2i00000000000000000000000000
χ402222222-2-22-2-2-22-2-2-2-2-222200-2002−2i−2i2i2i2-2-200002i2i−2i−2i-20000002−2i2i00002i−2i00000000000000000000000000
χ412222-22222-222-2-200-2222202202200000-20022220000-22222-2-2000000000-2-20000-2-2000000000000000000
χ422222-22222-222-2-200-2222202202200000-200-2-2-2-20000-2-2-2-2-2-2-200000000022000022000000000000000000
χ432222-22222-222-2-200-222220-2-20-2-200000-20022220000-2-2-2-2-222000000000-2-2000022000000000000000000
χ442222-22222-222-2-200-222220-2-20-2-200000-200-2-2-2-20000-2222222000000000220000-2-2000000000000000000
χ452222-222-2-2-2-2-22-200222-2-20220-2-2000002002i2i−2i−2i0000-22i2i−2i−2i2-2000000000−2i2i0000−2i2i000000000000000000
χ462222-222-2-2-2-2-22-200222-2-20220-2-200000200−2i−2i2i2i0000-2−2i−2i2i2i2-20000000002i−2i00002i−2i000000000000000000
χ472222-222-2-2-2-2-22-200222-2-20-2-2022000002002i2i−2i−2i0000-2−2i−2i2i2i-22000000000−2i2i00002i−2i000000000000000000
χ482222-222-2-2-2-2-22-200222-2-20-2-202200000200−2i−2i2i2i0000-22i2i−2i−2i-220000000002i−2i0000−2i2i000000000000000000
χ492-22-202-22i−2i02i−2i000002-22i−2i02-202i−2i01+i−1−i1−i−1+i0002ζ3−2ζ32ζ−2ζ1+i−1−i1−i−1+i02ζ3−2ζ32ζ−2ζ00000i2−i22−200001+i−1−i1−i−1+i000000i2−i22−20000000000
χ502-22-202-22i−2i02i−2i000002-22i−2i02-202i−2i01+i−1−i1−i−1+i000−2ζ32ζ3−2ζ2ζ1+i−1−i1−i−1+i0−2ζ32ζ3−2ζ2ζ00000−i2i2−2200001+i−1−i1−i−1+i000000−i2i2−220000000000
χ512-22-202-22i−2i02i−2i000002-22i−2i02-202i−2i0−1−i1+i−1+i1−i0002ζ3−2ζ32ζ−2ζ−1−i1+i−1+i1−i02ζ3−2ζ32ζ−2ζ00000−i2i2−220000−1−i1+i−1+i1−i000000−i2i2−220000000000
χ522-22-202-22i−2i02i−2i000002-22i−2i02-202i−2i0−1−i1+i−1+i1−i000−2ζ32ζ3−2ζ2ζ−1−i1+i−1+i1−i0−2ζ32ζ3−2ζ2ζ00000i2−i22−20000−1−i1+i−1+i1−i000000i2−i22−20000000000
χ532-22-202-22i−2i02i−2i000002-22i−2i0-220−2i2i01+i−1−i1−i−1+i0002ζ3−2ζ32ζ−2ζ1+i−1−i1−i−1+i0−2ζ32ζ3−2ζ2ζ00000i2−i22−20000−1−i1+i−1+i1−i000000−i2i2−220000000000
χ542-22-202-22i−2i02i−2i000002-22i−2i0-220−2i2i01+i−1−i1−i−1+i000−2ζ32ζ3−2ζ2ζ1+i−1−i1−i−1+i02ζ3−2ζ32ζ−2ζ00000−i2i2−220000−1−i1+i−1+i1−i000000i2−i22−20000000000
χ552-22-202-22i−2i02i−2i000002-22i−2i0-220−2i2i0−1−i1+i−1+i1−i0002ζ3−2ζ32ζ−2ζ−1−i1+i−1+i1−i0−2ζ32ζ3−2ζ2ζ00000−i2i2−2200001+i−1−i1−i−1+i000000i2−i22−20000000000
χ562-22-202-22i−2i02i−2i000002-22i−2i0-220−2i2i0−1−i1+i−1+i1−i000−2ζ32ζ3−2ζ2ζ−1−i1+i−1+i1−i02ζ3−2ζ32ζ−2ζ00000i2−i22−200001+i−1−i1−i−1+i000000−i2i2−220000000000
χ572-22-202-2−2i2i0−2i2i000002-2−2i2i02-20−2i2i01−i−1+i1+i−1−i0002ζ−2ζ2ζ3−2ζ31−i−1+i1+i−1−i02ζ−2ζ2ζ3−2ζ300000i2−i2−2200001−i−1+i1+i−1−i000000i2−i2−220000000000
χ582-22-202-2−2i2i0−2i2i000002-2−2i2i02-20−2i2i01−i−1+i1+i−1−i000−2ζ2ζ−2ζ32ζ31−i−1+i1+i−1−i0−2ζ2ζ−2ζ32ζ300000−i2i22−200001−i−1+i1+i−1−i000000−i2i22−20000000000
χ592-22-202-2−2i2i0−2i2i000002-2−2i2i02-20−2i2i0−1+i1−i−1−i1+i0002ζ−2ζ2ζ3−2ζ3−1+i1−i−1−i1+i02ζ−2ζ2ζ3−2ζ300000−i2i22−20000−1+i1−i−1−i1+i000000−i2i22−20000000000
χ602-22-202-2−2i2i0−2i2i000002-2−2i2i02-20−2i2i0−1+i1−i−1−i1+i000−2ζ2ζ−2ζ32ζ3−1+i1−i−1−i1+i0−2ζ2ζ−2ζ32ζ300000i2−i2−220000−1+i1−i−1−i1+i000000i2−i2−220000000000
χ612-22-202-2−2i2i0−2i2i000002-2−2i2i0-2202i−2i01−i−1+i1+i−1−i0002ζ−2ζ2ζ3−2ζ31−i−1+i1+i−1−i0−2ζ2ζ−2ζ32ζ300000i2−i2−220000−1+i1−i−1−i1+i000000−i2i22−20000000000
χ622-22-202-2−2i2i0−2i2i000002-2−2i2i0-2202i−2i01−i−1+i1+i−1−i000−2ζ2ζ−2ζ32ζ31−i−1+i1+i−1−i02ζ−2ζ2ζ3−2ζ300000−i2i22−20000−1+i1−i−1−i1+i000000i2−i2−220000000000
χ632-22-202-2−2i2i0−2i2i000002-2−2i2i0-2202i−2i0−1+i1−i−1−i1+i0002ζ−2ζ2ζ3−2ζ3−1+i1−i−1−i1+i0−2ζ2ζ−2ζ32ζ300000−i2i22−200001−i−1+i1+i−1−i000000i2−i2−220000000000
χ642-22-202-2−2i2i0−2i2i000002-2−2i2i0-2202i−2i0−1+i1−i−1−i1+i000−2ζ2ζ−2ζ32ζ3−1+i1−i−1−i1+i02ζ−2ζ2ζ3−2ζ300000i2−i2−2200001−i−1+i1+i−1−i000000−i2i22−20000000000
χ6544444-4-4444-4-4-4-44440000-400-4004000000000000000000000000000000000000000000000000000000000
χ6644444-4-4444-4-4-4-4-4-440000400400-4000000000000000000000000000000000000000000000000000000000
χ6744444-4-4-4-44444-444-40000400-400-4000000000000000000000000000000000000000000000000000000000
χ6844444-4-4-4-44444-4-4-4-40000-4004004000000000000000000000000000000000000000000000000000000000
χ694444-44444-444-4-400-4-4-4-4-40000000000040000000000400000000000000000000000000000000000000000
χ704444-444-4-4-4-4-44-4004-4-44400000000000-40000000000400000000000000000000000000000000000000000
χ714444-4-4-444-4-4-44400-4000000000000000000000000000000000000000000000000002i2−2i22i2−2i200000000000000
χ724444-4-4-444-4-4-44400-400000000000000000000000000000000000000000000000000−2i22i2−2i22i200000000000000
χ734444-4-4-4-4-4-444-440040000000000000000000000000000000000000000000000000022−22−222200000000000000
χ744444-4-4-4-4-4-444-4400400000000000000000000000000000000000000000000000000−222222−2200000000000000
χ754-44-404-44i−4i04i−4i00000-44−4i4i00000002+2i−2−2i2−2i−2+2i0000000−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000000000
χ764-44-404-44i−4i04i−4i00000-44−4i4i0000000−2−2i2+2i−2+2i2−2i00000002+2i−2−2i2−2i−2+2i000000000000000000000000000000000000000000
χ774-44-404-4−4i4i0−4i4i00000-444i−4i00000002−2i−2+2i2+2i−2−2i0000000−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000000000
χ784-44-404-4−4i4i0−4i4i00000-444i−4i0000000−2+2i2−2i−2−2i2+2i00000002−2i−2+2i2+2i−2−2i000000000000000000000000000000000000000000
χ798-88-80-888i−8i0−8i8i0000000000000000000000000000000000000000000000000000000000000000000000000
χ808-88-80-88−8i8i08i−8i0000000000000000000000000000000000000000000000000000000000000000000000000
χ818-8-8880000-8000000000000000000000004i2−4i200000000000000000000000000000000000000000000000000
χ828-8-8880000-800000000000000000000000−4i24i200000000000000000000000000000000000000000000000000
χ838-8-88-80000800008-8000000000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-8000080000-88000000000000000000000000000000000000000000000000000000000000000000000
χ851616-16-16000000000000000000000000000000000000000000000000000000000000000000000000000000000

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