Finite Group Databasebeta

← Group #349939

Character table — Group #349939

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222222244444444444444444444444444444444444444444444444888888888888888824
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
χ51111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-111-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-111-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-222-2-2222222222200000000-2-2-2-2-20000-2-2-2-200000000000000000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-2-2-2-200000000-2-2-2-2-20000222200000000000000000000000000
χ19222222222222-2-222-2-222-2-2000000002222222222-2-2-2-2-2-2-2000000000000000000000000000000
χ20222222222222-2-222-2-222-2-200000000-2-2-2-2-2-2-2-222-2-2-22222000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-20000000000000000-2-22220000000022-2-222-2-2000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-20000000000000000-2-222200000000-2-222-2-222000000000000000000
χ2322222222-2-2-2-222-2-222-2-2-2-22222-2-2-2-20000000022-2-220000-2-22200000000000000000000000000
χ2422222222-2-2-2-222-2-222-2-2-2-2-2-2-2-222220000000022-2-22000022-2-200000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-22222000000002222-2-2-2-2-2-2-2-22-2-222000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-2222200000000-2-2-2-22222-2-2-2-2222-2-2000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22200000000000000002222-20000000022-2-2-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22200000000000000002222-200000000-2-22222-2-2000000000000000000
χ29222-2-2-2-2200002-22-22-22-20000002i2i−2i−2i00002i2i−2i−2i002-20002i−2i002i−2i2-22-20000000000000000000000
χ30222-2-2-2-2200002-22-22-22-20000002i2i−2i−2i0000−2i−2i2i2i002-2000−2i2i002i−2i-22-220000000000000000000000
χ31222-2-2-2-2200002-22-22-22-2000000−2i−2i2i2i00002i2i−2i−2i002-20002i−2i00−2i2i-22-220000000000000000000000
χ32222-2-2-2-2200002-22-22-22-2000000−2i−2i2i2i0000−2i−2i2i2i002-2000−2i2i00−2i2i2-22-20000000000000000000000
χ33222-2-2-2-2200002-2-222-2-220000002i2i−2i−2i2i2i−2i−2i000000-2202i−2i0000−2i2i00002-22-2000000000000000000
χ34222-2-2-2-2200002-2-222-2-220000002i2i−2i−2i−2i−2i2i2i000000-220−2i2i0000−2i2i0000-22-22000000000000000000
χ35222-2-2-2-2200002-2-222-2-22000000−2i−2i2i2i2i2i−2i−2i000000-2202i−2i00002i−2i0000-22-22000000000000000000
χ36222-2-2-2-2200002-2-222-2-22000000−2i−2i2i2i−2i−2i2i2i000000-220−2i2i00002i−2i00002-22-2000000000000000000
χ37222-2-2-2-220000-222-2-222-2002i2i−2i−2i000000002i2i−2i−2i00-22000−2i2i2i−2i0000002-2-22000000000000000000
χ38222-2-2-2-220000-222-2-222-2002i2i−2i−2i00000000−2i−2i2i2i00-220002i−2i2i−2i000000-222-2000000000000000000
χ39222-2-2-2-220000-222-2-222-200−2i−2i2i2i000000002i2i−2i−2i00-22000−2i2i−2i2i000000-222-2000000000000000000
χ40222-2-2-2-220000-222-2-222-200−2i−2i2i2i00000000−2i−2i2i2i00-220002i−2i−2i2i0000002-2-22000000000000000000
χ41222-2-2-2-220000-22-22-22-22002i2i−2i−2i00002i2i−2i−2i0000002-20−2i2i00−2i2i002-2-220000000000000000000000
χ42222-2-2-2-220000-22-22-22-22002i2i−2i−2i0000−2i−2i2i2i0000002-202i−2i00−2i2i00-222-20000000000000000000000
χ43222-2-2-2-220000-22-22-22-2200−2i−2i2i2i00002i2i−2i−2i0000002-20−2i2i002i−2i00-222-20000000000000000000000
χ44222-2-2-2-220000-22-22-22-2200−2i−2i2i2i0000−2i−2i2i2i0000002-202i−2i002i−2i002-2-220000000000000000000000
χ4522-222-2-2-222-2-2-2-20022002-22-22-22-22-200000000000000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2000000
χ4622-222-2-2-222-2-2-2-20022002-22-22-22-22-200000000000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2000000
χ4722-222-2-2-222-2-2-2-20022002-2-22-22-22-2200000000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2000000
χ4822-222-2-2-222-2-2-2-20022002-2-22-22-22-2200000000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2000000
χ4922-222-2-2-2-2-222-2-2002200-222-22-2-22-2200000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ5022-222-2-2-2-2-222-2-2002200-222-22-2-22-2200000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ5122-222-2-2-2-2-222-2-2002200-22-22-222-22-200000000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ5222-222-2-2-2-2-222-2-2002200-22-22-222-22-200000000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ532-2-22-22-222-22-2002200-2-200000000002i−2i2i−2i2i−2i2i−2i2-200000000000000000002−22−22−22−20000i2−i2i2−i200
χ542-2-22-22-222-22-2002200-2-200000000002i−2i2i−2i2i−2i2i−2i2-20000000000000000000−22−22−22−220000−i2i2−i2i200
χ552-2-22-22-222-22-2002200-2-20000000000−2i2i−2i2i−2i2i−2i2i2-200000000000000000002−22−22−22−20000−i2i2−i2i200
χ562-2-22-22-222-22-2002200-2-20000000000−2i2i−2i2i−2i2i−2i2i2-20000000000000000000−22−22−22−220000i2−i2i2−i200
χ572-2-22-22-22-22-22002200-2-200000000002i−2i2i−2i−2i2i−2i2i-2200000000000000000002−22−2−22−220000i2−i2−i2i200
χ582-2-22-22-22-22-22002200-2-200000000002i−2i2i−2i−2i2i−2i2i-220000000000000000000−22−222−22−20000−i2i2i2−i200
χ592-2-22-22-22-22-22002200-2-20000000000−2i2i−2i2i2i−2i2i−2i-2200000000000000000002−22−2−22−220000−i2i2i2−i200
χ602-2-22-22-22-22-22002200-2-20000000000−2i2i−2i2i2i−2i2i−2i-220000000000000000000−22−222−22−20000i2−i2−i2i200
χ6144-444-4-4-444-4-44400-4-400-440000000000000000000000000000000000000000000000000000000
χ6244-444-4-4-4-4-4444400-4-4004-40000000000000000000000000000000000000000000000000000000
χ6344-4-4-444-400004-400-4400004i−4i−4i4i000000000000000000000000000000000000000000000000000
χ6444-4-4-444-400004-400-440000−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ6544-4-4-444-40000-44004-4000000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ6644-4-4-444-40000-44004-400000000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ674-444-4-44-44-4-44000000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ684-444-4-44-44-4-4400000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ694-444-4-44-4-444-4000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ704-444-4-44-4-444-400000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ714-4-44-44-444-44-400-4-40044000000000000000000-440000000000000000000000000000000000000
χ724-4-44-44-44-44-4400-4-400440000000000000000004-40000000000000000000000000000000000000
χ734-4-4-44-4440000004-400-44000000000000004-4-44000000000000000000000000000000000000000
χ744-4-4-44-4440000004-400-4400000000000000-444-4000000000000000000000000000000000000000
χ754-4-4-44-444000000-44004-400000000004-4-440000000000000000000000000000000000000000000
χ764-4-4-44-444000000-44004-40000000000-444-40000000000000000000000000000000000000000000
χ778-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000000

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