Finite Group Databasebeta

← Group #101679

Character table — Group #101679

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222222244444444444444888888888888888822444444488888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i11-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1ii−i−iii−i−i1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i11-1-1-111-1-1ii−i−iii−i−i-1-1-1-11111−i−iii−i−iii-11
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1-1-111-1-111ii−i−i−i−iii1111-1-1-1-1−i−iiiii−i−i-11
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1-1-111-1-111ii−i−i−i−iii-1-1-1-11111ii−i−i−i−iii1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-111-1-111−i−iiiii−i−i1111-1-1-1-1ii−i−i−i−iii-11
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-111-1-111−i−iiiii−i−i-1-1-1-11111−i−iiiii−i−i1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii11-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−iii−i−iii1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii11-1-1-111-1-1−i−iii−i−iii-1-1-1-11111ii−i−iii−i−i-11
χ1722222222222222-2-222-2-22-2-2-2-22000000000000000022-222-2-2-2-200000000000000000000000000
χ1822222222222222-2-222-2-22-2-2-2-220000000000000000-2-2-2-2-2222200000000000000000000000000
χ19222222222222-2-222-2-222-2-2-222-2222222220000000000-2000000-2-2-2-20000000000000000000000
χ20222222222222-2-222-2-222-2-2-222-2-2-2-2-2-2-2-2-20000000000-200000022220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-222-2-2-2000000002i2i2i2i−2i−2i−2i−2i0020000000000−2i−2i2i2i000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-222-2-2-200000000−2i−2i−2i−2i2i2i2i2i00200000000002i2i−2i−2i000000000000000000
χ2322222222-2-2-2-222222222-222-2-2-2000000002222222200-20000000000-2-2-2-2000000000000000000
χ2422222222-2-2-2-222222222-222-2-2-200000000-2-2-2-2-2-2-2-200-200000000002222000000000000000000
χ2522222222-2-2-2-222-2-222-2-2-2-2-222-22i2i2i2i−2i−2i−2i−2i00000000002000000−2i−2i2i2i0000000000000000000000
χ2622222222-2-2-2-222-2-222-2-2-2-2-222-2−2i−2i−2i−2i2i2i2i2i000000000020000002i2i−2i−2i0000000000000000000000
χ2722222222-2-2-2-2-2-222-2-2222-2-2-2-220000000000000000222-2-2-2-22200000000000000000000000000
χ2822222222-2-2-2-2-2-222-2-2222-2-2-2-220000000000000000-2-222222-2-200000000000000000000000000
χ2922-222-2-2-222-2-22200-2-20020000-222−2−222−2−222−2−222−2−22-202-200002−22−22−22−2000000000000000000
χ3022-222-2-2-222-2-22200-2-20020000-222−2−222−2−2−2−222−2−222-220-2200002−22−2−22−22000000000000000000
χ3122-222-2-2-222-2-22200-2-20020000-2−2−222−2−22222−2−222−2−2-220-220000−22−222−22−2000000000000000000
χ3222-222-2-2-222-2-22200-2-20020000-2−2−222−2−222−2−222−2−2222-202-20000−22−22−22−22000000000000000000
χ3322-222-2-2-222-2-2-2-2002200-20000222−2−222−2−2i2i2−i2−i2−i2−i2i2i2000002i−2i2i−2i−22−22−i2i2i2−i2000000000000000000
χ3422-222-2-2-222-2-2-2-2002200-20000222−2−222−2−2−i2−i2i2i2i2i2−i2−i200000−2i2i−2i2i−22−22i2−i2−i2i2000000000000000000
χ3522-222-2-2-222-2-2-2-2002200-200002−2−222−2−222i2i2−i2−i2−i2−i2i2i200000−2i2i−2i2i2−22−2−i2i2i2−i2000000000000000000
χ3622-222-2-2-222-2-2-2-2002200-200002−2−222−2−222−i2−i2i2i2i2i2−i2−i2000002i−2i2i−2i2−22−2i2−i2−i2i2000000000000000000
χ3722-222-2-2-2-2-2222200-2-200-200002i2i2−i2−i2−i2−i2i2i222−2−222−2−200000−2i2i2i−2i−i2i2i2−i2−22−22000000000000000000
χ3822-222-2-2-2-2-2222200-2-200-200002i2i2−i2−i2−i2−i2i2i2−2−222−2−222000002i−2i−2i2i−i2i2i2−i22−22−2000000000000000000
χ3922-222-2-2-2-2-2222200-2-200-200002−i2−i2i2i2i2i2−i2−i222−2−222−2−2000002i−2i−2i2ii2−i2−i2i2−22−22000000000000000000
χ4022-222-2-2-2-2-2222200-2-200-200002−i2−i2i2i2i2i2−i2−i2−2−222−2−22200000−2i2i2i−2ii2−i2−i2i22−22−2000000000000000000
χ4122-222-2-2-2-2-222-2-200220020000-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-20-220000i2−i2−i2i2i2−i2−i2i2000000000000000000
χ4222-222-2-2-2-2-222-2-200220020000-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2-2202-20000i2−i2−i2i2−i2i2i2−i2000000000000000000
χ4322-222-2-2-2-2-222-2-200220020000-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2-2202-20000−i2i2i2−i2i2−i2−i2i2000000000000000000
χ4422-222-2-2-2-2-222-2-200220020000-2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22-20-220000−i2i2i2−i2−i2i2i2−i2000000000000000000
χ4522-2-2-222-200002i−2i2i−2i2i−2i2i−2i02-2000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000022−2−2i2i2−i2−i21+i−1−i1−i−1+i000000
χ4622-2-2-222-200002i−2i2i−2i2i−2i2i−2i02-2000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000−2−222−i2−i2i2i2−1−i1+i−1+i1−i000000
χ4722-2-2-222-200002i−2i2i−2i2i−2i2i−2i02-200000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000022−2−2i2i2−i2−i2−1−i1+i−1+i1−i000000
χ4822-2-2-222-200002i−2i2i−2i2i−2i2i−2i02-200000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000−2−222−i2−i2i2i21+i−1−i1−i−1+i000000
χ4922-2-2-222-20000−2i2i−2i2i−2i2i−2i2i02-2000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000022−2−2−i2−i2i2i2−1+i1−i−1−i1+i000000
χ5022-2-2-222-20000−2i2i−2i2i−2i2i−2i2i02-2000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000−2−222i2i2−i2−i21−i−1+i1+i−1−i000000
χ5122-2-2-222-20000−2i2i−2i2i−2i2i−2i2i02-200000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000022−2−2−i2−i2i2i21−i−1+i1+i−1−i000000
χ5222-2-2-222-20000−2i2i−2i2i−2i2i−2i2i02-200000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000−2−222i2i2−i2−i2−1+i1−i−1−i1+i000000
χ532-2-22-2-2222-22-2002200-2-20002-202i−2i2i−2i2i−2i2i−2i00000000000000000000000002−22−22−22−20000i2−i2i2−i200
χ542-2-22-2-2222-22-2002200-2-20002-202i−2i2i−2i2i−2i2i−2i0000000000000000000000000−22−22−22−220000−i2i2−i2i200
χ552-2-22-2-2222-22-2002200-2-20002-20−2i2i−2i2i−2i2i−2i2i00000000000000000000000002−22−22−22−20000−i2i2−i2i200
χ562-2-22-2-2222-22-2002200-2-20002-20−2i2i−2i2i−2i2i−2i2i0000000000000000000000000−22−22−22−220000i2−i2i2−i200
χ572-2-22-2-222-22-2200-2-200220002-202-22-2-22-2200000000000000000000000002−22−2−22−2200002−2−2200
χ582-2-22-2-222-22-2200-2-200220002-202-22-2-22-220000000000000000000000000−22−222−22−20000−222−200
χ592-2-22-2-222-22-2200-2-200220002-20-22-222-22-200000000000000000000000002−22−2−22−220000−222−200
χ602-2-22-2-222-22-2200-2-200220002-20-22-222-22-20000000000000000000000000−22−222−22−200002−2−2200
χ61444-4-4-4-4400004i−4i00−4i4i00000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000
χ62444-4-4-4-4400004i−4i00−4i4i0000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000
χ63444-4-4-4-440000−4i4i004i−4i00000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000
χ64444-4-4-4-440000−4i4i004i−4i0000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000
χ6544-4-4-444-400004i−4i−4i4i4i−4i−4i4i0-44000000000000000000000000000000000000000000000000000000
χ6644-4-4-444-40000−4i4i4i−4i−4i4i4i−4i0-44000000000000000000000000000000000000000000000000000000
χ674-444-44-4-44-4-44000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ684-444-44-4-44-4-4400000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ694-444-44-4-4-444-40000000000000022−22−2222−222222−220000000000000000000000000000000000000000000
χ704-444-44-4-4-444-400000000000000−222222−2222−22−22220000000000000000000000000000000000000000000
χ714-44-44-44-40000004i−4i00−4i4i0000000000000000000000000000000000000002-2-222i−2i−2i2i0000000000
χ724-44-44-44-40000004i−4i00−4i4i000000000000000000000000000000000000000-222-2−2i2i2i−2i0000000000
χ734-44-44-44-4000000−4i4i004i−4i0000000000000000000000000000000000000002-2-22−2i2i2i−2i0000000000
χ744-44-44-44-4000000−4i4i004i−4i000000000000000000000000000000000000000-222-22i−2i−2i2i0000000000
χ754-4-44-4-4444-44-400-4-40044000-440000000000000000000000000000000000000000000000000000
χ764-4-44-4-444-44-44004400-4-4000-440000000000000000000000000000000000000000000000000000
χ778-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000

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