Finite Group Databasebeta

← Group #348728

Character table — Group #348728

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222244444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-111-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-11111-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-111111111-1-1-1-1-1-11111-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-1-1-111111-1-111-1-111-11111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-1-1-111111-1-111-1-111-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ17222222222222222-2-2-22-20000-2-2000022-222222222-20000-2-2-2-2-200000000000000000000000000
χ18222222222222222-2-2-22-20000-2-2000022-2-2-2-2-2-2-2-2-2-200002222-200000000000000000000000000
χ19222222222222-2-2-2222-222222222222-2-2-200000000-2-2-2-2-20000-200000000000000000000000000
χ20222222222222-2-2-2222-22-2-2-2-222-2-2-2-2-2-2-200000000-222220000-200000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-20000-2-20000-2-2200000000200000000222-2-222-2-2000000000000000000
χ22222222222222-2-2-2-2-2-2-2-20000-2-20000-2-22000000002000000002-2-222-2-222000000000000000000
χ2322222222-2-2-2-2222-2-2-22-20000220000-2-2-22222-2-2-2-2-20000-2-222200000000000000000000000000
χ2422222222-2-2-2-2222-2-2-22-20000220000-2-2-2-2-2-2-22222-2000022-2-2200000000000000000000000000
χ2522222222-2-2-2-2-2-2-2222-222222-2-2-2-2-2-222-200000000-2-2-2220000200000000000000000000000000
χ2622222222-2-2-2-2-2-2-2222-22-2-2-2-2-2-2222222-200000000-222-2-20000200000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000022000022200000000200000000-222-2-2-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2000022000022200000000200000000-2-2-22222-2-2000000000000000000
χ29222-2-2-2-2222-2-20002-2-20222-2-22-222-2-200000000000000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2000000
χ30222-2-2-2-2222-2-20002-2-20222-2-22-222-2-200000000000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2000000
χ31222-2-2-2-2222-2-20002-2-202-2-2222-2-2-22200000000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2000000
χ32222-2-2-2-2222-2-20002-2-202-2-2222-2-2-22200000000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2000000
χ33222-2-2-2-22-2-2220002-2-20222-2-2-22-2-22200000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ34222-2-2-2-22-2-2220002-2-20222-2-2-22-2-22200000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ35222-2-2-2-22-2-2220002-2-202-2-222-2222-2-200000000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ36222-2-2-2-22-2-2220002-2-202-2-222-2222-2-200000000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ372-2222-2-2-22-22-22-2-20002000000000002-202i2i−2i−2i2i2i−2i−2i0000000000000000002−22−22−22−20000i2−i2i2−i200
χ382-2222-2-2-22-22-22-2-20002000000000002-202i2i−2i−2i2i2i−2i−2i000000000000000000−22−22−22−220000−i2i2−i2i200
χ392-2222-2-2-22-22-22-2-20002000000000002-20−2i−2i2i2i−2i−2i2i2i0000000000000000002−22−22−22−20000−i2i2−i2i200
χ402-2222-2-2-22-22-22-2-20002000000000002-20−2i−2i2i2i−2i−2i2i2i000000000000000000−22−22−22−220000i2−i2i2−i200
χ412-2222-2-2-2-22-222-2-2000200000000000-2202i2i−2i−2i−2i−2i2i2i0000000000000000002−22−2−22−220000i2−i2−i2i200
χ422-2222-2-2-2-22-222-2-2000200000000000-2202i2i−2i−2i−2i−2i2i2i000000000000000000−22−222−22−20000−i2i2i2−i200
χ432-2222-2-2-2-22-222-2-2000200000000000-220−2i−2i2i2i2i2i−2i−2i0000000000000000002−22−2−22−220000−i2i2i2−i200
χ442-2222-2-2-2-22-222-2-2000200000000000-220−2i−2i2i2i2i2i−2i−2i000000000000000000−22−222−22−20000i2−i2−i2i200
χ452-2-22-22-22000022-222-2-2-20000002i−2i2i−2i00-200002i−2i2i−2i2002i−2i002i−2i02-22-20000000000000000000000
χ462-2-22-22-22000022-222-2-2-20000002i−2i2i−2i00-20000−2i2i−2i2i2002i−2i00−2i2i0-22-220000000000000000000000
χ472-2-22-22-22000022-222-2-2-2000000−2i2i−2i2i00-200002i−2i2i−2i200−2i2i002i−2i0-22-220000000000000000000000
χ482-2-22-22-22000022-222-2-2-2000000−2i2i−2i2i00-20000−2i2i−2i2i200−2i2i00−2i2i02-22-20000000000000000000000
χ492-2-22-22-22000022-2-2-22-222-22-200000000200002i−2i2i−2i-22-20000−2i2i000002i−2i2i−2i000000000000000000
χ502-2-22-22-22000022-2-2-22-222-22-20000000020000−2i2i−2i2i-22-200002i−2i00000−2i2i−2i2i000000000000000000
χ512-2-22-22-22000022-2-2-22-22-22-2200000000200002i−2i2i−2i-2-220000−2i2i00000−2i2i−2i2i000000000000000000
χ522-2-22-22-22000022-2-2-22-22-22-220000000020000−2i2i−2i2i-2-2200002i−2i000002i−2i2i−2i000000000000000000
χ532-2-22-22-220000-2-2222-22-20000002i−2i2i−2i0022-22-20000-200−2i2i2-200000002i−2i−2i2i000000000000000000
χ542-2-22-22-220000-2-2222-22-20000002i−2i2i−2i002-22-220000-200−2i2i-220000000−2i2i2i−2i000000000000000000
χ552-2-22-22-220000-2-2222-22-2000000−2i2i−2i2i0022-22-20000-2002i−2i2-20000000−2i2i2i−2i000000000000000000
χ562-2-22-22-220000-2-2222-22-2000000−2i2i−2i2i002-22-220000-2002i−2i-2200000002i−2i−2i2i000000000000000000
χ572-2-22-22-220000-2-22-2-22222-22-200000000-22-22-200002-2200-220002-2-220000000000000000000000
χ582-2-22-22-220000-2-22-2-22222-22-200000000-2-22-2200002-22002-2000-222-20000000000000000000000
χ592-2-22-22-220000-2-22-2-2222-22-2200000000-22-22-2000022-200-22000-222-20000000000000000000000
χ602-2-22-22-220000-2-22-2-2222-22-2200000000-2-22-22000022-2002-20002-2-220000000000000000000000
χ61444-4-4-4-4444-4-4000-4440-40000-44000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44-4-444000-4440-400004-4000000000000000000000000000000000000000000000000000
χ6344-44-4-44-400004-44000-40000000000000000004-4-44000000000000000000000000000000000000
χ6444-44-4-44-400004-44000-4000000000000000000-444-4000000000000000000000000000000000000
χ6544-44-4-44-40000-44-40004000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ6644-44-4-44-40000-44-4000400000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ674-4444-4-4-44-44-4-444000-400000000000-44000000000000000000000000000000000000000000000
χ684-4444-4-4-4-44-44-444000-4000000000004-4000000000000000000000000000000000000000000000
χ694-44-4-444-44-4-44000000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ704-44-4-444-44-4-4400000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ714-44-4-444-4-444-4000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ724-44-4-444-4-444-400000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ734-4-4-44-44400000004-440-40000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ744-4-4-44-44400000004-440-4000000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ754-4-4-44-4440000000-44-4044-4-4400000000000000000000000000000000000000000000000000000
χ764-4-4-44-4440000000-44-404-444-400000000000000000000000000000000000000000000000000000
χ7788-8-888-8-8000000000000000000000000000000000000000000000000000000000000000000000

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