Finite Group Databasebeta

← Group #100437

Character table — Group #100437

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222222244444444444444444444448888888844444888888888888888888884444888844
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
χ511111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-111-1-111-1-1-1-1-11111-1-1-1-111-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ1011111111-1-1-1-111-1-111-1-1-1-1-11111-1-1-1-111-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111-11
χ1111111111-1-1-1-111-1-111-1-1-1-1-11111-1-1-1-111-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111-11
χ1211111111-1-1-1-111-1-111-1-1-1-1-11111-1-1-1-111-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-11-1
χ1311111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1111111-1iiii−i−i−i−i1-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1-11
χ1411111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1111111-1iiii−i−i−i−i1-1-111ii−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1111-1
χ1511111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1111111-1−i−i−i−iiiii1-1-111−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1111-1
χ1611111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1111111-1−i−i−i−iiiii1-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11
χ1722222222222222-2-222-2-22-2-22222-2-2-2-2-2-2200000000-2-2-222000000000000000000000000000000
χ1822222222222222-2-222-2-22-2-2-2-2-2-22222-2-2200000000-222-2-2000000000000000000000000000000
χ19222222222222-2-222-2-222-2-2-20000000022-222222222-20000-2-2-2-200000000000000000000000000
χ20222222222222-2-222-2-222-2-2-20000000022-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-22200000000-2-2-2000000002000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-22200000000-2-2-200000000200000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2322222222-2-2-2-222222222-22222222222-2-2-200000000-2-2-2-2-2000000000000000000000000000000
χ2422222222-2-2-2-222222222-222-2-2-2-2-2-2-2-2-2-2-200000000-22222000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-2222-2-200000000-2-220000000020000000022-2-2-2-222000000000000000000
χ2622222222-2-2-2-2-2-222-2-2222-2-200000000-2-2200000000200000000-2-22222-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222000000002222i2i2i2i−2i−2i−2i−2i-20000−2i−2i2i2i00000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222200000000222−2i−2i−2i−2i2i2i2i2i-200002i2i−2i−2i00000000000000000000000000
χ29222-22-2-2-222-2-22200-2-200200000022-2-200-222−2−222−2−202-2002−22−22−22−22−22−2000000000000000000
χ30222-22-2-2-222-2-22200-2-200200000022-2-200-2−2−222−2−22202-200−22−22−22−22−22−22000000000000000000
χ31222-22-2-2-222-2-22200-2-2002000000-2-22200-222−2−222−2−20-22002−22−2−22−22−22−22000000000000000000
χ32222-22-2-2-222-2-22200-2-2002000000-2-22200-2−2−222−2−2220-2200−22−222−22−22−22−2000000000000000000
χ33222-22-2-2-222-2-2-2-2002200-2002i2i−2i−2i000000222−2−222−2−20002i−2i−22−22i2−i2−i2i2i2−i2−i2i2000000000000000000
χ34222-22-2-2-222-2-2-2-2002200-2002i2i−2i−2i0000002−2−222−2−2220002i−2i2−22−2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ35222-22-2-2-222-2-2-2-2002200-200−2i−2i2i2i000000222−2−222−2−2000−2i2i−22−22−i2i2i2−i2−i2i2i2−i2000000000000000000
χ36222-22-2-2-222-2-2-2-2002200-200−2i−2i2i2i0000002−2−222−2−222000−2i2i2−22−2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ37222-22-2-2-2-2-2222200-2-200-200000022-2-2002i2i2−i2−i2−i2−i2i2i20-2200i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ38222-22-2-2-2-2-2222200-2-200-200000022-2-2002−i2−i2i2i2i2i2−i2−i20-2200−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ39222-22-2-2-2-2-2222200-2-200-2000000-2-222002i2i2−i2−i2−i2−i2i2i202-200i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ40222-22-2-2-2-2-2222200-2-200-2000000-2-222002−i2−i2i2i2i2i2−i2−i202-200−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ41222-22-2-2-2-2-222-2-20022002002i2i−2i−2i000000-2i2i2−i2−i2−i2−i2i2i2000−2i2i−i2i2i2−i2−222−22−2−22000000000000000000
χ42222-22-2-2-2-2-222-2-20022002002i2i−2i−2i000000-2−i2−i2i2i2i2i2−i2−i2000−2i2ii2−i2−i2i22−2−22−222−2000000000000000000
χ43222-22-2-2-2-2-222-2-2002200200−2i−2i2i2i000000-2i2i2−i2−i2−i2−i2i2i20002i−2i−i2i2i2−i22−2−22−222−2000000000000000000
χ44222-22-2-2-2-2-222-2-2002200200−2i−2i2i2i000000-2−i2−i2i2i2i2i2−i2−i20002i−2ii2−i2−i2i2−222−22−2−22000000000000000000
χ4522-2-2-22-222-22-200-2-20022000000000002-202i−2i2i−2i2i−2i2i−2i0000000000000000022−2−222−2−20000i2−i2i2−i200
χ4622-2-2-22-222-22-200-2-20022000000000002-202i−2i2i−2i2i−2i2i−2i00000000000000000−2−222−2−2220000−i2i2−i2i200
χ4722-2-2-22-222-22-200-2-20022000000000002-20−2i2i−2i2i−2i2i−2i2i0000000000000000022−2−222−2−20000−i2i2−i2i200
χ4822-2-2-22-222-22-200-2-20022000000000002-20−2i2i−2i2i−2i2i−2i2i00000000000000000−2−222−2−2220000i2−i2i2−i200
χ4922-2-2-22-22-22-22002200-2-2000000000002-202-22-2-22-2200000000000000000i2i2−i2−i2−i2−i2i2i20000−i2i2i2−i200
χ5022-2-2-22-22-22-22002200-2-2000000000002-202-22-2-22-2200000000000000000−i2−i2i2i2i2i2−i2−i20000i2−i2−i2i200
χ5122-2-2-22-22-22-22002200-2-2000000000002-20-22-222-22-200000000000000000i2i2−i2−i2−i2−i2i2i20000i2−i2−i2i200
χ5222-2-2-22-22-22-22002200-2-2000000000002-20-22-222-22-200000000000000000−i2−i2i2i2i2i2−i2−i20000−i2i2i2−i200
χ532-22-2-222-200002-22i−2i2-22i−2i02i−2i2-22-22i−2i2i−2i00000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1−i−1+i000000
χ542-22-2-222-200002-22i−2i2-22i−2i02i−2i2-22-22i−2i2i−2i0000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1+i1−i000000
χ552-22-2-222-200002-22i−2i2-22i−2i02i−2i-22-22−2i2i−2i2i00000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1+i1−i000000
χ562-22-2-222-200002-22i−2i2-22i−2i02i−2i-22-22−2i2i−2i2i0000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1−i−1+i000000
χ572-22-2-222-200002-2−2i2i2-2−2i2i0−2i2i2-22-2−2i2i−2i2i00000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1+i−1−i000000
χ582-22-2-222-200002-2−2i2i2-2−2i2i0−2i2i2-22-2−2i2i−2i2i0000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1−i1+i000000
χ592-22-2-222-200002-2−2i2i2-2−2i2i0−2i2i-22-222i−2i2i−2i00000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1−i1+i000000
χ602-22-2-222-200002-2−2i2i2-2−2i2i0−2i2i-22-222i−2i2i−2i0000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1+i−1−i000000
χ6144-44-4-44-44-4-4400000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ6244-44-4-44-44-4-440000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ6344-44-4-44-4-444-4000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ6444-44-4-44-4-444-40000000000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ6544-4-4-44-444-44-4004400-4-400000000000-4400000000000000000000000000000000000000000000
χ6644-4-4-44-44-44-4400-4-4004400000000000-4400000000000000000000000000000000000000000000
χ674-444-4-4-4400004-400-440000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ684-444-4-4-4400004-400-44000000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ694-444-4-4-440000-44004-4000004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ704-444-4-4-440000-44004-400000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ714-44-4-444-40000-444i−4i-444i−4i0−4i4i000000000000000000000000000000000000000000000000000000
χ724-44-4-444-40000-44−4i4i-44−4i4i04i−4i000000000000000000000000000000000000000000000000000000
χ734-4-4444-4-40000004i−4i00−4i4i0000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000000000
χ744-4-4444-4-40000004i−4i00−4i4i000000000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000000000
χ754-4-4444-4-4000000−4i4i004i−4i0000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000
χ764-4-4444-4-4000000−4i4i004i−4i000000000000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000
χ778-8-8-88-888000000000000000000000000000000000000000000000000000000000000000000000

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