Finite Group Databasebeta

← Group #349469

Character table — Group #349469

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111111111-1-1-1-111-1-11111-1-1-1-111111-1-1-1-1-1-11-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111111111-1-1-1-111-1-11111-1-1-1-111111-1-1-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111111111-1-1-1-111-1-11111-1-1-1-11-1-1-1-11111-1-11-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ1211111111111111-1-1-1-111-1-11111-1-1-1-11-1-1-1-11111-1-11-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ1311111111111111-1-1-1-111-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ1411111111111111-1-1-1-111-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ1511111111111111-1-1-1-111-1-1-1-1-1-111111-1-1-1-11111-1-11-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111111111-1-1-1-111-1-1-1-1-1-111111-1-1-1-11111-1-11-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222-2-2-222222-22222222222-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000
χ1822222222222-2-2-222222-222-2-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000000000000000000000
χ1922222222222-2-2-2-2-2-2-22-2-2-22222-2-2-2-2-20000000022-22-2-222000000000000000000000000000000
χ2022222222222-2-2-2-2-2-2-22-2-2-2-2-2-2-22222-20000000022-2222-2-2000000000000000000000000000000
χ2122222222-2-2-22222222-22-2-200000000-22222222222-2-20000-2-2-2-200000000000000000000000000
χ2222222222-2-2-22222222-22-2-200000000-2-2-2-2-2-2-2-2-222-2-20000222200000000000000000000000000
χ2322222222-2-2-2222-2-2-2-2-222200000000-22222-2-2-2-2-2-2-220000-2-22200000000000000000000000000
χ2422222222-2-2-2222-2-2-2-2-222200000000-2-2-2-2-22222-2-2-22000022-2-200000000000000000000000000
χ2522222222-2-2-2-2-2-22222-2-2-2-200000000200000000-2-2220000000022-2-222-2-2000000000000000000
χ2622222222-2-2-2-2-2-22222-2-2-2-200000000200000000-2-22200000000-2-222-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22200000000200000000222-20000000022-2-2-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200000000200000000222-200000000-2-22222-2-2000000000000000000
χ29222-2-2-2-222-2-200022-2-2202-222-2-222-2-200000000000000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2000000
χ30222-2-2-2-222-2-200022-2-2202-222-2-222-2-200000000000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2000000
χ31222-2-2-2-222-2-200022-2-2202-2-2-222-2-22200000000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2000000
χ32222-2-2-2-222-2-200022-2-2202-2-2-222-2-22200000000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2000000
χ33222-2-2-2-222-2-2000-2-22220-2222-2-2-2-22200000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ34222-2-2-2-222-2-2000-2-22220-2222-2-2-2-22200000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ35222-2-2-2-222-2-2000-2-22220-22-2-22222-2-200000000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ36222-2-2-2-222-2-2000-2-22220-22-2-22222-2-200000000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ3722-22-22-2-222-222-20000-2-20000002-22-22000022-2-200-20002-2002-22-22-20000000000000000000000
χ3822-22-22-2-222-222-20000-2-20000002-22-220000-2-22200-20002-200-22-22-220000000000000000000000
χ3922-22-22-2-222-222-20000-2-2000000-22-222000022-2-200-2000-22002-2-22-220000000000000000000000
χ4022-22-22-2-222-222-20000-2-2000000-22-2220000-2-22200-2000-2200-222-22-20000000000000000000000
χ4122-22-22-2-222-2-2-220000-220000002-22-2-22i2i−2i−2i0000002000-222i−2i0000002i−2i2i−2i000000000000000000
χ4222-22-22-2-222-2-2-220000-220000002-22-2-2−2i−2i2i2i0000002000-22−2i2i000000−2i2i−2i2i000000000000000000
χ4322-22-22-2-222-2-2-220000-22000000-22-22-22i2i−2i−2i00000020002-22i−2i000000−2i2i−2i2i000000000000000000
χ4422-22-22-2-222-2-2-220000-22000000-22-22-2−2i−2i2i2i00000020002-2−2i2i0000002i−2i2i−2i000000000000000000
χ4522-22-22-2-2-2-2222-200002-2002i−2i2i−2i0000-2000022-2-200202i−2i0000-2200002i−2i−2i2i000000000000000000
χ4622-22-22-2-2-2-2222-200002-2002i−2i2i−2i0000-20000-2-22200202i−2i00002-20000−2i2i2i−2i000000000000000000
χ4722-22-22-2-2-2-2222-200002-200−2i2i−2i2i0000-2000022-2-20020−2i2i0000-220000−2i2i2i−2i000000000000000000
χ4822-22-22-2-2-2-2222-200002-200−2i2i−2i2i0000-20000-2-2220020−2i2i00002-200002i−2i−2i2i000000000000000000
χ4922-22-22-2-2-2-22-2-22000022002i−2i2i−2i000022i2i−2i−2i000000-20−2i2i00−2i2i002-2-220000000000000000000000
χ5022-22-22-2-2-2-22-2-22000022002i−2i2i−2i00002−2i−2i2i2i000000-20−2i2i002i−2i00-222-20000000000000000000000
χ5122-22-22-2-2-2-22-2-2200002200−2i2i−2i2i000022i2i−2i−2i000000-202i−2i00−2i2i00-222-20000000000000000000000
χ5222-22-22-2-2-2-22-2-2200002200−2i2i−2i2i00002−2i−2i2i2i000000-202i−2i002i−2i002-2-220000000000000000000000
χ532-2-2-2-22220002-222-22-20-2000000000002i−2i2i−2i2i−2i2i−2i2-20000000000000000002−22−22−22−20000i2−i2i2−i200
χ542-2-2-2-22220002-222-22-20-2000000000002i−2i2i−2i2i−2i2i−2i2-2000000000000000000−22−22−22−220000−i2i2−i2i200
χ552-2-2-2-22220002-222-22-20-200000000000−2i2i−2i2i−2i2i−2i2i2-20000000000000000002−22−22−22−20000−i2i2−i2i200
χ562-2-2-2-22220002-222-22-20-200000000000−2i2i−2i2i−2i2i−2i2i2-2000000000000000000−22−22−22−220000i2−i2i2−i200
χ572-2-2-2-22220002-22-22-220-2000000000002i−2i2i−2i−2i2i−2i2i-220000000000000000002−22−2−22−220000i2−i2−i2i200
χ582-2-2-2-22220002-22-22-220-2000000000002i−2i2i−2i−2i2i−2i2i-22000000000000000000−22−222−22−20000−i2i2i2−i200
χ592-2-2-2-22220002-22-22-220-200000000000−2i2i−2i2i2i−2i2i−2i-220000000000000000002−22−2−22−220000−i2i2i2−i200
χ602-2-2-2-22220002-22-22-220-200000000000−2i2i−2i2i2i−2i2i−2i-22000000000000000000−22−222−22−20000i2−i2−i2i200
χ61444-4-4-4-44-44400044-4-4-40-440000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44-444000-4-444-404-40000000000000000000000000000000000000000000000000000000
χ6344-4-44-44-44-440000000-400000004-4-4400000000000000000000000000000000000000000000000
χ6444-4-44-44-44-440000000-40000000-444-400000000000000000000000000000000000000000000000
χ6544-4-44-44-4-44-4000000040004i−4i−4i4i000000000000000000000000000000000000000000000000000
χ6644-4-44-44-4-44-400000004000−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ674-44-444-4-40004-4-40000040000000000000004i−4i−4i4i00000000000000000000000000000000000000
χ684-44-444-4-40004-4-4000004000000000000000−4i4i4i−4i00000000000000000000000000000000000000
χ694-44-444-4-4000-44400000-4000000000004-4-44000000000000000000000000000000000000000000
χ704-44-444-4-4000-44400000-400000000000-444-4000000000000000000000000000000000000000000
χ714-4-444-4-440000004-4-44000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ724-4-444-4-440000004-4-4400000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ734-4-444-4-44000000-444-4000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ744-4-444-4-44000000-444-400000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ754-4-4-4-4444000-44-44-44-4040000000000000000000-44000000000000000000000000000000000000
χ764-4-4-4-4444000-44-4-44-440400000000000000000004-4000000000000000000000000000000000000
χ778-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000000

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