Finite Group Databasebeta

← Group #348706

Character table — Group #348706

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444444444444422222244444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11-1
χ1011111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-11
χ1111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-11111-1-1-1-111-1-1-1-111-11
χ1211111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-11111-1-11-1
χ1311111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-11
χ1411111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1111-1
χ1511111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222-2-2-222222-222-2-22222222200000000-2-2-2-20000-200-2-2000000000000000000000000
χ1822222222222-2-2-222222-222-2-2-2-2-2-2-2-2-2-200000000-2-2220000-20022000000000000000000000000
χ1922222222222-2-2-2-2-2-2-22-2-2-2222222-2-2-2-200000000-2-2-2-2000020022000000000000000000000000
χ2022222222222-2-2-2-2-2-2-22-2-2-222-2-2-2-2222200000000-2-2220000200-2-2000000000000000000000000
χ2122222222-2-2-22222222-22-2-2220000000022222222-2-2000000-2-2-2000000-2-2000000000000000000
χ2222222222-2-2-22222222-22-2-22200000000-2-2-2-2-2-2-2-2-2-2000000-22200000022000000000000000000
χ2322222222-2-2-2222-2-2-2-2-2222-2-2000000002222-2-2-2-2-2-2000000222000000-2-2000000000000000000
χ2422222222-2-2-2222-2-2-2-2-2222-2-200000000-2-2-2-22222-2-20000002-2-200000022000000000000000000
χ2522222222-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000220022-2-22000022-2-200000000000000000000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-200000000000000002200-2-22220000-2-22200000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000220022-2-2-20000-2-22200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002200-2-222-2000022-2-200000000000000000000
χ29222-2-2-22-22-2-200022-2-2202-2002i2i−2i−2i2i2i−2i−2i000000000000000000000000000i2i2−i2−i2i2i2−i2−i22−22−2000000
χ30222-2-2-22-22-2-200022-2-2202-2002i2i−2i−2i2i2i−2i−2i000000000000000000000000000−i2−i2i2i2−i2−i2i2i2−22−22000000
χ31222-2-2-22-22-2-200022-2-2202-200−2i−2i2i2i−2i−2i2i2i000000000000000000000000000i2i2−i2−i2i2i2−i2−i2−22−22000000
χ32222-2-2-22-22-2-200022-2-2202-200−2i−2i2i2i−2i−2i2i2i000000000000000000000000000−i2−i2i2i2−i2−i2i2i22−22−2000000
χ33222-2-2-22-22-2-2000-2-22220-22002i2i−2i−2i−2i−2i2i2i000000000000000000000000000i2i2−i2−i2−i2−i2i2i22−2−22000000
χ34222-2-2-22-22-2-2000-2-22220-22002i2i−2i−2i−2i−2i2i2i000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−222−2000000
χ35222-2-2-22-22-2-2000-2-22220-2200−2i−2i2i2i2i2i−2i−2i000000000000000000000000000i2i2−i2−i2−i2−i2i2i2−222−2000000
χ36222-2-2-22-22-2-2000-2-22220-2200−2i−2i2i2i2i2i−2i−2i000000000000000000000000000−i2−i2i2i2i2i2−i2−i22−2−22000000
χ3722-2-22-2-2222-222-20000-2-2000000002i−2i2i−2i00002i2i−2i−2i-22002-22-202i−2i2i−2i000000000000000000000000
χ3822-2-22-2-2222-222-20000-2-2000000002i−2i2i−2i0000−2i−2i2i2i-2200-22-220−2i2i2i−2i000000000000000000000000
χ3922-2-22-2-2222-222-20000-2-200000000−2i2i−2i2i00002i2i−2i−2i-2200-22-2202i−2i−2i2i000000000000000000000000
χ4022-2-22-2-2222-222-20000-2-200000000−2i2i−2i2i0000−2i−2i2i2i-22002-22-20−2i2i−2i2i000000000000000000000000
χ4122-2-22-2-2222-2-2-220000-22000000002i−2i2i−2i22-2-200002-2000000000−2i2i2i−2i2i−2i2-2000000000000000000
χ4222-2-22-2-2222-2-2-220000-22000000002i−2i2i−2i-2-22200002-2000000000−2i2i−2i2i−2i2i-22000000000000000000
χ4322-2-22-2-2222-2-2-220000-2200000000−2i2i−2i2i22-2-200002-20000000002i−2i−2i2i−2i2i2-2000000000000000000
χ4422-2-22-2-2222-2-2-220000-2200000000−2i2i−2i2i-2-22200002-20000000002i−2i2i−2i2i−2i-22000000000000000000
χ4522-2-22-2-22-2-2222-200002-200002-22-2000000002i2i−2i−2i2-22-200000−2i2i002i−2i−2i2i00000000000000000000
χ4622-2-22-2-22-2-2222-200002-200002-22-200000000−2i−2i2i2i2-22-2000002i−2i00−2i2i2i−2i00000000000000000000
χ4722-2-22-2-22-2-2222-200002-20000-22-22000000002i2i−2i−2i2-2-2200000−2i2i00−2i2i2i−2i00000000000000000000
χ4822-2-22-2-22-2-2222-200002-20000-22-2200000000−2i−2i2i2i2-2-22000002i−2i002i−2i−2i2i00000000000000000000
χ4922-2-22-2-22-2-22-2-2200002200002-22-2000022-2-20000-22-222-2-22000000000-22000000000000000000
χ5022-2-22-2-22-2-22-2-2200002200002-22-20000-2-2220000-22-22-222-20000000002-2000000000000000000
χ5122-2-22-2-22-2-22-2-220000220000-22-22000022-2-20000-222-2-222-2000000000-22000000000000000000
χ5222-2-22-2-22-2-22-2-220000220000-22-220000-2-2220000-222-22-2-220000000002-2000000000000000000
χ532-2-2-2222-20002-222-22-20-2002-2000000002-22-22-22-20000000000000000000i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i200
χ542-2-2-2222-20002-222-22-20-2002-2000000002-22-22-22-20000000000000000000−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i200
χ552-2-2-2222-20002-222-22-20-2002-200000000-22-22-22-220000000000000000000i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i200
χ562-2-2-2222-20002-222-22-20-2002-200000000-22-22-22-220000000000000000000−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i200
χ572-2-2-2222-20002-22-22-220-200-22000000002-22-2-22-220000000000000000000i2−i2i2−i2−i2i2−i2i20000i2−i2−i2i200
χ582-2-2-2222-20002-22-22-220-200-22000000002-22-2-22-220000000000000000000−i2i2−i2i2i2−i2i2−i20000−i2i2i2−i200
χ592-2-2-2222-20002-22-22-220-200-2200000000-22-222-22-20000000000000000000i2−i2i2−i2−i2i2−i2i20000−i2i2i2−i200
χ602-2-2-2222-20002-22-22-220-200-2200000000-22-222-22-20000000000000000000−i2i2−i2i2i2−i2i2−i20000i2−i2−i2i200
χ61444-4-4-44-4-44400044-4-4-40-440000000000000000000000000000000000000000000000000000000
χ62444-4-4-44-4-444000-4-444-404-40000000000000000000000000000000000000000000000000000000
χ6344-44-44-4-44-440000000-40000000004-4-44000000000000000000000000000000000000000000000
χ6444-44-44-4-44-440000000-4000000000-444-4000000000000000000000000000000000000000000000
χ6544-44-44-4-4-44-400000004000004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ6644-44-44-4-4-44-40000000400000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ674-4444-4-4-40004-4-400000400000000000000004i−4i−4i4i0000000000000000000000000000000000000
χ684-4444-4-4-40004-4-40000040000000000000000−4i4i4i−4i0000000000000000000000000000000000000
χ694-4444-4-4-4000-44400000-40000000000004-4-4400000000000000000000000000000000000000000
χ704-4444-4-4-4000-44400000-4000000000000-444-400000000000000000000000000000000000000000
χ714-4-44-4-4440000004-4-44000000000000000000000000000000000000000002-2-222-2-220000000000
χ724-4-44-4-4440000004-4-4400000000000000000000000000000000000000000-222-2-222-20000000000
χ734-4-44-4-444000000-444-4000000000000000000000000000000000000000002-2-22-222-20000000000
χ744-4-44-4-444000000-444-400000000000000000000000000000000000000000-222-22-2-220000000000
χ754-4-4-4444-4000-44-44-44-40400-4400000000000000000000000000000000000000000000000000000
χ764-4-4-4444-4000-44-4-44-4404004-400000000000000000000000000000000000000000000000000000
χ778-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000

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