Finite Group Databasebeta

← Group #100491

Character table — Group #100491

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222244444444448888888844444888888888888888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1111-1-1-1-111111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1111-1-1-1-111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-111-1iiii−i−i−i−i-1-1111ii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ1011111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-111-1iiii−i−i−i−i-1-1111ii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111-11
χ1111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-111-1−i−i−i−iiiii-1-1111−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111-11
χ1211111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-111-1−i−i−i−iiiii-1-1111−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-11-1
χ1311111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1iiii−i−i−i−i111-1-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1-11
χ1411111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1iiii−i−i−i−i111-1-1ii−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1111-1
χ1511111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1−i−i−i−iiiii111-1-1−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1111-1
χ1611111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1−i−i−i−iiiii111-1-1−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11
χ172222222222222-2-2222-2-222222-2-2-2-2-2-2-2-220000000022-2-2-2000000000000000000000000000000
χ182222222222222-2-2222-2-2-2-2-2-22-2-22222-2-2200000000-2-2-222000000000000000000000000000000
χ1922222222222-2-222-2-22222222-2222222-2-2-200000000-2-2-2-2-2000000000000000000000000000000
χ2022222222222-2-222-2-2222-2-2-2-2-222-2-2-2-2-2-2-20000000022-222000000000000000000000000000000
χ2122222222-2-2-2222222-2220000-2-2-2000022-22222222200-200-2-2-2-200000000000000000000000000
χ2222222222-2-2-2222222-2220000-2-2-2000022-2-2-2-2-2-2-2-2-200-200222200000000000000000000000000
χ2322222222-2-2-222-2-222-2-2-20000-2220000-2-2-2000000000020000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ2422222222-2-2-222-2-222-2-2-20000-2220000-2-2-200000000002000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2522222222-2-2-2-2-222-2-2-22200002-2-20000-2-220000000000200000022-2-2-2-222000000000000000000
χ2622222222-2-2-2-2-222-2-2-22200002-2-20000-2-2200000000002000000-2-22222-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000022200002222i2i2i2i−2i−2i−2i−2i00-200−2i−2i2i2i00000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200002220000222−2i−2i−2i−2i2i2i2i2i00-2002i2i−2i−2i00000000000000000000000000
χ29222-22-2-2-222-2002200-2-2-222-2-202-222-2-2000000000000000000000000000022−2−222−2−22−22−2000000
χ30222-22-2-2-222-2002200-2-2-222-2-202-222-2-20000000000000000000000000000−2−222−2−222−22−22000000
χ31222-22-2-2-222-2002200-2-2-2-2-22202-2-2-222000000000000000000000000000022−2−222−2−2−22−22000000
χ32222-22-2-2-222-2002200-2-2-2-2-22202-2-2-2220000000000000000000000000000−2−222−2−2222−22−2000000
χ33222-22-2-2-222-200-2-200-22222-2-20-22-2-2220000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ34222-22-2-2-222-200-2-200-22222-2-20-22-2-2220000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ35222-22-2-2-222-200-2-200-222-2-2220-2222-2-20000000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ36222-22-2-2-222-200-2-200-222-2-2220-2222-2-20000000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ3722-22-22-2-22-222200-2-2-2002-22-2200000000-222−2−222−2−22-20002−22−22−22−22−22−2000000000000000000
χ3822-22-22-2-22-222200-2-2-2002-22-2200000000-2−2−222−2−2222-2000−22−22−22−22−22−22000000000000000000
χ3922-22-22-2-22-222200-2-2-200-22-22200000000-222−2−222−2−2-220002−22−2−22−22−22−22000000000000000000
χ4022-22-22-2-22-222200-2-2-200-22-22200000000-2−2−222−2−222-22000−22−222−22−22−22−2000000000000000000
χ4122-22-22-2-22-22-2-20022-2002-22-2-2000000002i2i2−i2−i2−i2−i2i2i2-22000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ4222-22-22-2-22-22-2-20022-2002-22-2-2000000002−i2−i2i2i2i2i2−i2−i2-22000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ4322-22-22-2-22-22-2-20022-200-22-22-2000000002i2i2−i2−i2−i2−i2i2i22-2000i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ4422-22-22-2-22-22-2-20022-200-22-22-2000000002−i2−i2i2i2i2i2−i2−i22-2000−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ4522-22-22-2-2-22-22200-2-22000000-2002i−2i2i−2i00222−2−222−2−20002i−2i−22−22i2−i2−i2i2i2−i2−i2i2000000000000000000
χ4622-22-22-2-2-22-22200-2-22000000-2002i−2i2i−2i002−2−222−2−2220002i−2i2−22−2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ4722-22-22-2-2-22-22200-2-22000000-200−2i2i−2i2i00222−2−222−2−2000−2i2i−22−22−i2i2i2−i2−i2i2i2−i2000000000000000000
χ4822-22-22-2-2-22-22200-2-22000000-200−2i2i−2i2i002−2−222−2−222000−2i2i2−22−2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ4922-22-22-2-2-22-2-2-2002220000002002i−2i2i−2i00-2i2i2−i2−i2−i2−i2i2i2000−2i2i−i2i2i2−i22−2−22−222−2000000000000000000
χ5022-22-22-2-2-22-2-2-2002220000002002i−2i2i−2i00-2−i2−i2i2i2i2i2−i2−i2000−2i2ii2−i2−i2i2−222−22−2−22000000000000000000
χ5122-22-22-2-2-22-2-2-200222000000200−2i2i−2i2i00-2i2i2−i2−i2−i2−i2i2i20002i−2i−i2i2i2−i2−222−22−2−22000000000000000000
χ5222-22-22-2-2-22-2-2-200222000000200−2i2i−2i2i00-2−i2−i2i2i2i2i2−i2−i20002i−2ii2−i2−i2i22−2−22−222−2000000000000000000
χ532-222-2-2-220002i−2i2i−2i2i−2i02i−2i000000000002-202ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000i2−i22−200
χ542-222-2-2-220002i−2i2i−2i2i−2i02i−2i000000000002-202ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−i2i2−2200
χ552-222-2-2-220002i−2i2i−2i2i−2i02i−2i000000000002-20−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000−i2i2−2200
χ562-222-2-2-220002i−2i2i−2i2i−2i02i−2i000000000002-20−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000i2−i22−200
χ572-222-2-2-22000−2i2i−2i2i−2i2i0−2i2i000000000002-202ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000i2−i2−2200
χ582-222-2-2-22000−2i2i−2i2i−2i2i0−2i2i000000000002-202ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000−i2i22−200
χ592-222-2-2-22000−2i2i−2i2i−2i2i0−2i2i000000000002-20−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000−i2i22−200
χ602-222-2-2-22000−2i2i−2i2i−2i2i0−2i2i000000000002-20−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000i2−i2−2200
χ61444-44-4-4-4-4-440044004-4-400000-4400000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-4-4400-4-400444000004-400000000000000000000000000000000000000000000000000
χ6344-4-4-4-4444-4-40000004004-4-4400000000000000000000000000000000000000000000000000000
χ6444-4-4-4-4444-4-4000000400-444-400000000000000000000000000000000000000000000000000000
χ6544-4-4-4-444-444000000-40000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ6644-4-4-4-444-444000000-4000000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ674-444-4-4-440004i−4i−4i4i4i−4i0−4i4i00000000000-4400000000000000000000000000000000000000000000
χ684-444-4-4-44000−4i4i4i−4i−4i4i04i−4i00000000000-4400000000000000000000000000000000000000000000
χ694-44-4-444-4000004i−4i000−4i4i0000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000
χ704-44-4-444-4000004i−4i000−4i4i000000000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000
χ714-44-4-444-400000−4i4i0004i−4i0000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000
χ724-44-4-444-400000−4i4i0004i−4i000000000000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000
χ734-4-444-44-40004i−4i00−4i4i000000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000
χ744-4-444-44-40004i−4i00−4i4i00000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000
χ754-4-444-44-4000−4i4i004i−4i000000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000
χ764-4-444-44-4000−4i4i004i−4i00000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000
χ778-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000

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