Finite Group Databasebeta

← Group #100320

Character table — Group #100320

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888844444888888888888888888888888888844
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
χ51111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1111-1-1-1-1-1-11-111-1-1-11111-1-1-1-1-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ1011111111-1111-1-1-1-1-1-11-111-1-1-11111-1-1-1-1-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111-11
χ1111111111-1111-1-1-1-1-1-11-111-1-1-11111-1-1-1-1-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111-11
χ1211111111-1111-1-1-1-1-1-11-111-1-1-11111-1-1-1-1-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-11-1
χ1311111111-1111-1-1-1-1-1-11-111-1-1-1-1-1-1-11111-1iiii−i−i−i−i1-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1-11
χ1411111111-1111-1-1-1-1-1-11-111-1-1-1-1-1-1-11111-1iiii−i−i−i−i1-1-111ii−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1111-1
χ1511111111-1111-1-1-1-1-1-11-111-1-1-1-1-1-1-11111-1−i−i−i−iiiii1-1-111−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1111-1
χ1611111111-1111-1-1-1-1-1-11-111-1-1-1-1-1-1-11111-1−i−i−i−iiiii1-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11
χ17222222222222-2-2-22222-2-2-222-222222222-200000000-2-2-2-2-2000000000000000000000000000000
χ18222222222222-2-2-22222-2-2-222-2-2-2-2-2-2-2-2-2-200000000-22222000000000000000000000000000000
χ19222222222-2-2-2222222-2222-2-2-200000000-222222222-20000-2-2-2-200000000000000000000000000
χ20222222222-2-2-2222222-2222-2-2-200000000-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ21222222222-2-2-2-2-2-2222-2-2-2-2-2-220000000020000000020000000022-2-222-2-2000000000000000000
χ22222222222-2-2-2-2-2-2222-2-2-2-2-2-2200000000200000000200000000-2-222-2-222000000000000000000
χ2322222222-2222222-2-2-222-2-2-2-222222-2-2-2-2200000000-2-2-222000000000000000000000000000000
χ2422222222-2222222-2-2-222-2-2-2-22-2-2-2-22222200000000-222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2222-2-2-2-22-2-222-200000000-2000000002000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ2622222222-2-2-2-2222-2-2-2-22-2-222-200000000-200000000200000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222220000000022i2i2i2i−2i−2i−2i−2i-20000−2i−2i2i2i00000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222000000002−2i−2i−2i−2i2i2i2i2i-200002i2i−2i−2i00000000000000000000000000
χ29222-2-2-2-2220002-2-22-2-2022-200000000000022-2-222-2-200000000000000000i2i2−i2−i2i2i2−i2−i20000i2−i2i2−i200
χ30222-2-2-2-2220002-2-22-2-2022-200000000000022-2-222-2-200000000000000000−i2−i2i2i2−i2−i2i2i20000−i2i2−i2i200
χ31222-2-2-2-2220002-2-22-2-2022-2000000000000-2-222-2-22200000000000000000i2i2−i2−i2i2i2−i2−i20000−i2i2−i2i200
χ32222-2-2-2-2220002-2-22-2-2022-2000000000000-2-222-2-22200000000000000000−i2−i2i2i2−i2−i2i2i20000i2−i2i2−i200
χ33222-2-2-2-22-2000-222-2220-22-20000000000002i2i−2i−2i−2i−2i2i2i0000000000000000022−2−2−2−2220000−i2i2i2−i200
χ34222-2-2-2-22-2000-222-2220-22-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000000−2−22222−2−20000i2−i2−i2i200
χ35222-2-2-2-22-2000-222-2220-22-2000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000022−2−2−2−2220000i2−i2−i2i200
χ36222-2-2-2-22-2000-222-2220-22-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000−2−22222−2−20000−i2i2i2−i200
χ3722-222-2-2-222-2-2000-2-2220002-202i2i−2i−2i2i2i−2i−2i00000000000000000000000000i2−i2i2−i2i2−i2i2−i22−22−2000000
χ3822-222-2-2-222-2-2000-2-2220002-202i2i−2i−2i2i2i−2i−2i00000000000000000000000000−i2i2−i2i2−i2i2−i2i2−22−22000000
χ3922-222-2-2-222-2-2000-2-2220002-20−2i−2i2i2i−2i−2i2i2i00000000000000000000000000i2−i2i2−i2i2−i2i2−i2−22−22000000
χ4022-222-2-2-222-2-2000-2-2220002-20−2i−2i2i2i−2i−2i2i2i00000000000000000000000000−i2i2−i2i2−i2i2−i2i22−22−2000000
χ4122-222-2-2-2-22-2-200022-22000-2202i2i−2i−2i−2i−2i2i2i000000000000000000000000002−22−2−22−22−i2i2i2−i2000000
χ4222-222-2-2-2-22-2-200022-22000-2202i2i−2i−2i−2i−2i2i2i00000000000000000000000000−22−222−22−2i2−i2−i2i2000000
χ4322-222-2-2-2-22-2-200022-22000-220−2i−2i2i2i2i2i−2i−2i000000000000000000000000002−22−2−22−22i2−i2−i2i2000000
χ4422-222-2-2-2-22-2-200022-22000-220−2i−2i2i2i2i2i−2i−2i00000000000000000000000000−22−222−22−2−i2i2i2−i2000000
χ452-2-22-22-22022-222-2000-2-20000-200002i−2i2i−2i2i2−i2i2−i2i2−i2i2−i202i−2i00i2−i2i2−i22−22−22−22−2000000000000000000
χ462-2-22-22-22022-222-2000-2-20000-200002i−2i2i−2i2−i2i2−i2i2−i2i2−i2i202i−2i00−i2i2−i2i2−22−22−22−22000000000000000000
χ472-2-22-22-22022-222-2000-2-20000-20000−2i2i−2i2i2i2−i2i2−i2i2−i2i2−i20−2i2i00i2−i2i2−i2−22−22−22−22000000000000000000
χ482-2-22-22-22022-222-2000-2-20000-20000−2i2i−2i2i2−i2i2−i2i2−i2i2−i2i20−2i2i00−i2i2−i2i22−22−22−22−2000000000000000000
χ492-2-22-22-22022-2-2-22000-220000200002i−2i2i−2i-22−22−2−22−220−2i2i002−2−22i2−i2i2−i2−i2i2−i2i2000000000000000000
χ502-2-22-22-22022-2-2-22000-220000200002i−2i2i−2i-2−22−222−22−20−2i2i00−222−2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ512-2-22-22-22022-2-2-22000-22000020000−2i2i−2i2i-22−22−2−22−2202i−2i002−2−22−i2i2−i2i2i2−i2i2−i2000000000000000000
χ522-2-22-22-22022-2-2-22000-22000020000−2i2i−2i2i-2−22−222−22−202i−2i00−222−2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ532-2-22-22-220-2-2222-20002-2000022-22-20000-2i2−i2i2−i2i2−i2i2−i20002-2−i2i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000000000
χ542-2-22-22-220-2-2222-20002-2000022-22-20000-2−i2i2−i2i2−i2i2−i2i20002-2i2−i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000000000
χ552-2-22-22-220-2-2222-20002-200002-22-220000-2i2−i2i2−i2i2−i2i2−i2000-22−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000000000
χ562-2-22-22-220-2-2222-20002-200002-22-220000-2−i2i2−i2i2−i2i2−i2i2000-22i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000000000
χ572-2-22-22-220-2-22-2-22000220000-22-22-2000022−22−2−22−22000-22−222−22−2−222−2−22000000000000000000
χ582-2-22-22-220-2-22-2-22000220000-22-22-200002−22−222−22−2000-222−2−22−222−2−222−2000000000000000000
χ592-2-22-22-220-2-22-2-22000220000-2-22-22000022−22−2−22−220002-2−222−2−222−2−222−2000000000000000000
χ602-2-22-22-220-2-22-2-22000220000-2-22-2200002−22−222−22−20002-22−2−222−2−222−2−22000000000000000000
χ61444-4-4-4-444000-4444-4-40-4-440000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44-40004-4-4-44404-440000000000000000000000000000000000000000000000000000000
χ6344-444-4-4-44-444000-4-44-4000-4400000000000000000000000000000000000000000000000000000
χ6444-444-4-4-4-4-44400044-4-40004-400000000000000000000000000000000000000000000000000000
χ6544-4-4-444-44000000-44-4000000000000000000000000000000000000000002-2-222-2-220000000000
χ6644-4-4-444-44000000-44-400000000000000000000000000000000000000000-222-2-222-20000000000
χ6744-4-4-444-4-40000004-44000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ6844-4-4-444-4-40000004-4400000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ694-444-4-44-404-44000000-400000000004-4-4400000000000000000000000000000000000000000000
χ704-444-4-44-404-44000000-40000000000-444-400000000000000000000000000000000000000000000
χ714-444-4-44-40-44-400000040000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ724-444-4-44-40-44-40000004000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ734-4-4-44-44400004-440000-4000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ744-4-4-44-44400004-440000-400000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ754-4-4-44-4440000-44-4000040000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ764-4-4-44-4440000-44-40000400000000000000−222222−2222−22−222200000000000000000000000000000000000
χ778-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).