Finite Group Databasebeta

← Group #350125

Character table — Group #350125

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222222244444444444444444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-111-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-111-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-222-2-2222222222200000000-2-2-2-2-20000-2-2-2-200000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-2-2-22200000000-2-2-2-2-20000222200000000000000000000000000
χ19222222222222-2-222-2-22200000000-2-22222222222-2-2-2-2-2-2-2000000000000000000000000000000
χ20222222222222-2-222-2-22200000000-2-2-2-2-2-2-2-2-2-222-2-2-22222000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-200000000-2-22220000000022-2-222-2-2000000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-200000000-2-222200000000-2-222-2-222000000000000000000
χ2322222222-2-2-2-222-2-222-2-22222-2-2-2-2-2-20000000022-2-220000-2-22200000000000000000000000000
χ2422222222-2-2-2-222-2-222-2-2-2-2-2-22222-2-20000000022-2-22000022-2-200000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-22200000000222222-2-2-2-2-2-2-2-22-2-222000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-2220000000022-2-2-2-22222-2-2-2-2222-2-2000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000000022000000002222-20000000022-2-2-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000000022000000002222-200000000-2-22222-2-2000000000000000000
χ2922-2-2-22-2200002-22-22-22-200002i2i−2i−2i0000002i2i−2i−2i002-20002i−2i002i−2i2-22-20000000000000000000000
χ3022-2-2-22-2200002-22-22-22-200002i2i−2i−2i000000−2i−2i2i2i002-2000−2i2i002i−2i-22-220000000000000000000000
χ3122-2-2-22-2200002-22-22-22-20000−2i−2i2i2i0000002i2i−2i−2i002-20002i−2i00−2i2i-22-220000000000000000000000
χ3222-2-2-22-2200002-22-22-22-20000−2i−2i2i2i000000−2i−2i2i2i002-2000−2i2i00−2i2i2-22-20000000000000000000000
χ3322-2-2-22-2200002-2-222-2-2200002i2i−2i−2i002i2i−2i−2i000000-2202i−2i0000−2i2i00002-22-2000000000000000000
χ3422-2-2-22-2200002-2-222-2-2200002i2i−2i−2i00−2i−2i2i2i000000-220−2i2i0000−2i2i0000-22-22000000000000000000
χ3522-2-2-22-2200002-2-222-2-220000−2i−2i2i2i002i2i−2i−2i000000-2202i−2i00002i−2i0000-22-22000000000000000000
χ3622-2-2-22-2200002-2-222-2-220000−2i−2i2i2i00−2i−2i2i2i000000-220−2i2i00002i−2i00002-22-2000000000000000000
χ3722-2-2-22-220000-222-2-222-22i2i−2i−2i00000000002i2i−2i−2i00-22000−2i2i2i−2i0000002-2-22000000000000000000
χ3822-2-2-22-220000-222-2-222-22i2i−2i−2i0000000000−2i−2i2i2i00-220002i−2i2i−2i000000-222-2000000000000000000
χ3922-2-2-22-220000-222-2-222-2−2i−2i2i2i00000000002i2i−2i−2i00-22000−2i2i−2i2i000000-222-2000000000000000000
χ4022-2-2-22-220000-222-2-222-2−2i−2i2i2i0000000000−2i−2i2i2i00-220002i−2i−2i2i0000002-2-22000000000000000000
χ4122-2-2-22-220000-22-22-22-222i2i−2i−2i0000002i2i−2i−2i0000002-20−2i2i00−2i2i002-2-220000000000000000000000
χ4222-2-2-22-220000-22-22-22-222i2i−2i−2i000000−2i−2i2i2i0000002-202i−2i00−2i2i00-222-20000000000000000000000
χ4322-2-2-22-220000-22-22-22-22−2i−2i2i2i0000002i2i−2i−2i0000002-20−2i2i002i−2i00-222-20000000000000000000000
χ4422-2-2-22-220000-22-22-22-22−2i−2i2i2i000000−2i−2i2i2i0000002-202i−2i002i−2i002-2-220000000000000000000000
χ452-222-22-2-222-2-2-2-20022002-22-22-22-22-200000000000000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2000000
χ462-222-22-2-222-2-2-2-20022002-22-22-22-22-200000000000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2000000
χ472-222-22-2-222-2-2-2-2002200-22-22-22-222-200000000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2000000
χ482-222-22-2-222-2-2-2-2002200-22-22-22-222-200000000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2000000
χ492-222-22-2-2-2-222-2-20022002-22-2-22-22-2200000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ502-222-22-2-2-2-222-2-20022002-22-2-22-22-2200000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ512-222-22-2-2-2-222-2-2002200-22-222-22-2-2200000000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ522-222-22-2-2-2-222-2-2002200-22-222-22-2-2200000000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ532-22-2-2-2222-22-2002200-2-200000000002-22-22-22-22-20000000000000000000i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i200
χ542-22-2-2-2222-22-2002200-2-200000000002-22-22-22-22-20000000000000000000−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i200
χ552-22-2-2-2222-22-2002200-2-20000000000-22-22-22-222-20000000000000000000i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i200
χ562-22-2-2-2222-22-2002200-2-20000000000-22-22-22-222-20000000000000000000−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i200
χ572-22-2-2-222-22-22002200-2-200000000002-22-2-22-22-220000000000000000000i2−i2i2−i2−i2i2−i2i20000i2−i2−i2i200
χ582-22-2-2-222-22-22002200-2-200000000002-22-2-22-22-220000000000000000000−i2i2−i2i2i2−i2i2−i20000−i2i2i2−i200
χ592-22-2-2-222-22-22002200-2-20000000000-22-222-22-2-220000000000000000000i2−i2i2−i2−i2i2−i2i20000−i2i2i2−i200
χ602-22-2-2-222-22-22002200-2-20000000000-22-222-22-2-220000000000000000000−i2i2−i2i2i2−i2i2−i20000i2−i2−i2i200
χ61444-44-4-4-44-4-44000000000000000000000000000000000000000000000002-2-222-2-220000000000
χ62444-44-4-4-44-4-4400000000000000000000000000000000000000000000000-222-2-222-20000000000
χ63444-44-4-4-4-444-4000000000000000000000000000000000000000000000002-2-22-222-20000000000
χ64444-44-4-4-4-444-400000000000000000000000000000000000000000000000-222-22-2-220000000000
χ654-444-44-4-444-4-44400-4-40000000000-4400000000000000000000000000000000000000000000000
χ664-444-44-4-4-4-4444400-4-400000000004-400000000000000000000000000000000000000000000000
χ674-44-4-4-4444-44-400-4-40044000000000000000000-440000000000000000000000000000000000000
χ684-44-4-4-444-44-4400-4-400440000000000000000004-40000000000000000000000000000000000000
χ694-4-444-4-440000004-400-44000000000000004i−4i−4i4i000000000000000000000000000000000000000
χ704-4-444-4-440000004-400-4400000000000000−4i4i4i−4i000000000000000000000000000000000000000
χ714-4-444-4-44000000-44004-400000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ724-4-444-4-44000000-44004-40000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ734-4-4-4444-400004-400-44004i−4i−4i4i00000000000000000000000000000000000000000000000000000
χ744-4-4-4444-400004-400-4400−4i4i4i−4i00000000000000000000000000000000000000000000000000000
χ754-4-4-4444-40000-44004-40000004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ764-4-4-4444-40000-44004-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ7788-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000000

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