Finite Group Databasebeta

← Group #352425

Character table — Group #352425

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222222222222222222224444444444444444444444444444444444444444444444161616161616161632323232
order12222222444444444444444488888888888888884444444444444444444444888888888888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1
χ911111111-1-1-1-1111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ1011111111-1-1-1-1111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ1111111111-1-1-1-1111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ1211111111-1-1-1-1111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ1311111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ1411111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ1511111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-11
χ17222222222222222-2-2-2-2-2-2-2-220000000000000000-2-2222222-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000
χ18222222222222222-2-2-2-2-2-2-2-220000000000000000-2-222-2-2-2-22222-2-2-2-2-2-22222000000000000000000000000000000000000
χ19222222222222-2-2-222222222-22222222222222222-2-2-2-2000000000000-2-20000-2-2-2-2-2-2-2-20000000000000000000000000000
χ20222222222222-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000-2-20000222222220000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-2-2000000000000220000000000002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-2-200000000000022000000000000−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2322222222-2-2-2-22222222-2-2-2-220000000000000000-2-2-2-22222-2-2-2-2-2-2-2-2222222000000000000000000000000000000000000
χ2422222222-2-2-2-22222222-2-2-2-220000000000000000-2-2-2-2-2-2-2-22222222222-2-2-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-2-2-2-2-200000000000000002222000000000000-2-20000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2622222222-2-2-2-2-2-2-22222-2-2-2-2-200000000000000002222000000000000-2-2000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-22222-222222222-2-2-2-2-2-2-2-2-2-222000000000000220000-2-2-2-222220000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-222222222-2-2220000000000002200002222-2-2-2-20000000000000000000000000000
χ29222-2-2-22-222-2-200022-2-2-2-22202i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000000000i2−i2i2−i22−22−20000
χ30222-2-2-22-222-2-200022-2-2-2-22202i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000000000−i2i2−i2i2−22−220000
χ31222-2-2-22-222-2-200022-2-2-2-2220−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000i2−i2i2−i2−22−220000
χ32222-2-2-22-222-2-200022-2-2-2-2220−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000−i2i2−i2i22−22−20000
χ33222-2-2-22-2-2-222000-2-222-2-22202i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000i2−i2−i2i22−2−220000
χ34222-2-2-22-2-2-222000-2-222-2-22202i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000−i2i2i2−i2−222−20000
χ35222-2-2-22-2-2-222000-2-222-2-2220−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000000000i2−i2−i2i2−222−20000
χ36222-2-2-22-2-2-222000-2-222-2-2220−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000000000−i2i2i2−i22−2−220000
χ3722-222-2-2-2000022-200002-22-2-20000000022-2-222-2-22-20022-2-222-2-20000000000000022-2-20000000022-2-222-2-2000000000000
χ3822-222-2-2-2000022-200002-22-2-20000000022-2-222-2-22-200-2-222-2-2220000000000000022-2-200000000-2-222-2-222000000000000
χ3922-222-2-2-2000022-200002-22-2-200000000-2-222-2-2222-20022-2-222-2-200000000000000-2-22200000000-2-222-2-222000000000000
χ4022-222-2-2-2000022-200002-22-2-200000000-2-222-2-2222-200-2-222-2-22200000000000000-2-2220000000022-2-222-2-2000000000000
χ4122-222-2-2-2000022-20000-22-22-222-2-222-2-200000000-220022-2-2-2-222000000000022-2-2000022-2-222-2-200000000000000000000
χ4222-222-2-2-2000022-20000-22-22-222-2-222-2-200000000-2200-2-22222-2-2000000000022-2-20000-2-222-2-22200000000000000000000
χ4322-222-2-2-2000022-20000-22-22-2-2-222-2-22200000000-220022-2-2-2-2220000000000-2-2220000-2-222-2-22200000000000000000000
χ4422-222-2-2-2000022-20000-22-22-2-2-222-2-22200000000-2200-2-22222-2-20000000000-2-222000022-2-222-2-200000000000000000000
χ4522-222-2-2-20000-2-2200002-22-220000000022-2-222-2-2-2200000000002i2i−2i−2i002i2i−2i−2i0000-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4622-222-2-2-20000-2-2200002-22-220000000022-2-222-2-2-220000000000−2i−2i2i2i00−2i−2i2i2i0000-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4722-222-2-2-20000-2-2200002-22-2200000000-2-222-2-222-2200000000002i2i−2i−2i002i2i−2i−2i000022-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4822-222-2-2-20000-2-2200002-22-2200000000-2-222-2-222-220000000000−2i−2i2i2i00−2i−2i2i2i000022-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4922-222-2-2-20000-2-220000-22-22222-2-222-2-2000000002-200000000002i2i−2i−2i00−2i−2i2i2i-2-222000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ5022-222-2-2-20000-2-220000-22-22222-2-222-2-2000000002-20000000000−2i−2i2i2i002i2i−2i−2i-2-2220000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ5122-222-2-2-20000-2-220000-22-222-2-222-2-222000000002-200000000002i2i−2i−2i00−2i−2i2i2i22-2-20000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ5222-222-2-2-20000-2-220000-22-222-2-222-2-222000000002-20000000000−2i−2i2i2i002i2i−2i−2i22-2-2000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ532-222-22-2-22-22-22-2200000000-22−22−22−22−22−22−22−22−2002-22-22-200002-22-20000002−22−22−22−22−22−22−22−22−22−22−22−2000000000000
χ542-222-22-2-22-22-22-2200000000-22−22−22−22−22−22−22−22−2002-2-22-220000-22-220000002−22−22−22−2−22−22−22−22−22−22−22−22000000000000
χ552-222-22-2-22-22-22-2200000000-2−22−22−22−22−22−22−22−22002-22-22-200002-22-2000000−22−22−22−22−22−22−22−22−22−22−22−22000000000000
χ562-222-22-2-22-22-22-2200000000-2−22−22−22−22−22−22−22−22002-2-22-220000-22-22000000−22−22−22−222−22−22−22−22−22−22−22−2000000000000
χ572-222-22-2-22-22-2-22-20000000022−22−22−22−22−22−22−22−200-2200002i−2i2i−2i0000002i−2i2i−2i−22−22−22−22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ582-222-22-2-22-22-2-22-20000000022−22−22−22−22−22−22−22−200-220000−2i2i−2i2i000000−2i2i−2i2i−22−22−22−22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ592-222-22-2-22-22-2-22-2000000002−22−22−22−22−22−22−22−2200-2200002i−2i2i−2i0000002i−2i2i−2i2−22−22−22−2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ602-222-22-2-22-22-2-22-2000000002−22−22−22−22−22−22−22−2200-220000−2i2i−2i2i000000−2i2i−2i2i2−22−22−22−2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ612-222-22-2-2-22-222-2200000000-22−22−22−22−2−22−22−22−2200-222-22-20000-22-220000002−22−2−22−222−22−22−22−2−22−22−22−22000000000000
χ622-222-22-2-2-22-222-2200000000-22−22−22−22−2−22−22−22−2200-22-22-2200002-22-20000002−22−2−22−22−22−22−22−222−22−22−22−2000000000000
χ632-222-22-2-2-22-222-2200000000-2−22−22−22−222−22−22−22−200-222-22-20000-22-22000000−22−222−22−2−22−22−22−222−22−22−22−2000000000000
χ642-222-22-2-2-22-222-2200000000-2−22−22−22−222−22−22−22−200-22-22-2200002-22-2000000−22−222−22−22−22−22−22−2−22−22−22−22000000000000
χ652-222-22-2-2-22-22-22-20000000022−22−22−22−2−22−22−22−22002-200002i−2i2i−2i000000−2i2i−2i2i−22−222−22−2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ662-222-22-2-2-22-22-22-20000000022−22−22−22−2−22−22−22−22002-20000−2i2i−2i2i0000002i−2i2i−2i−22−222−22−2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ672-222-22-2-2-22-22-22-2000000002−22−22−22−222−22−22−22−2002-200002i−2i2i−2i000000−2i2i−2i2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ682-222-22-2-2-22-22-22-2000000002−22−22−22−222−22−22−22−2002-20000−2i2i−2i2i0000002i−2i2i−2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ692-2-22-2-22200002-2-22-22-2000022−2−222−2−222−2−222−2−2200002-2-22000000002-22-2-222−2−222−2−222−2−222−2−222−2−222−2−22000000000000
χ702-2-22-2-22200002-2-22-22-2000022−2−222−2−222−2−222−2−220000-222-2000000002-2-222-22−2−222−2−22−222−2−222−2−222−2−222−2000000000000
χ712-2-22-2-22200002-2-22-22-200002−222−2−222−2−222−2−222−200002-2-22000000002-22-2-22−222−2−222−2−222−2−222−2−222−2−222−2000000000000
χ722-2-22-2-22200002-2-22-22-200002−222−2−222−2−222−2−222−20000-222-2000000002-2-222-2−222−2−222−22−2−222−2−222−2−222−2−22000000000000
χ732-2-22-2-22200002-2-2-22-22000022−2−222−2−22−222−2−222−200002-2-2200000000-22-222-22−2−22−222−22−2−222−2−22−222−2−222−2000000000000
χ742-2-22-2-22200002-2-2-22-22000022−2−222−2−22−222−2−222−20000-222-200000000-222-2-222−2−22−222−2−222−2−222−22−2−222−2−22000000000000
χ752-2-22-2-22200002-2-2-22-2200002−222−2−222−22−2−222−2−2200002-2-2200000000-22-222-2−222−22−2−22−222−2−222−22−2−222−2−22000000000000
χ762-2-22-2-22200002-2-2-22-2200002−222−2−222−22−2−222−2−220000-222-200000000-222-2-22−222−22−2−222−2−222−2−22−222−2−222−2000000000000
χ772-2-22-2-2220000-2222-22-20000-22−2−222−2−222−2−222−2−22000000002i−2i−2i2i−2i2i2i−2i-220000−222−2−222−2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ782-2-22-2-2220000-2222-22-20000-22−2−222−2−222−2−222−2−2200000000−2i2i2i−2i2i−2i−2i2i-220000−222−2−222−2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ792-2-22-2-2220000-2222-22-20000-2−222−2−222−2−222−2−222−2000000002i−2i−2i2i−2i2i2i−2i-2200002−2−222−2−22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ802-2-22-2-2220000-2222-22-20000-2−222−2−222−2−222−2−222−200000000−2i2i2i−2i2i−2i−2i2i-2200002−2−222−2−22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ812-2-22-2-2220000-222-22-220000-22−2−222−2−22−222−2−222−2000000002i−2i−2i2i2i−2i−2i2i2-20000−222−22−2−22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ822-2-22-2-2220000-222-22-220000-22−2−222−2−22−222−2−222−200000000−2i2i2i−2i−2i2i2i−2i2-20000−222−22−2−22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ832-2-22-2-2220000-222-22-220000-2−222−2−222−22−2−222−2−22000000002i−2i−2i2i2i−2i−2i2i2-200002−2−22−222−2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ842-2-22-2-2220000-222-22-220000-2−222−2−222−22−2−222−2−2200000000−2i2i2i−2i−2i2i2i−2i2-200002−2−22−222−2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ85444-4-4-44-444-4-4000-4-44444-4-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ86444-4-4-44-4-4-44400044-4-444-4-4000000000000000000000000000000000000000000000000000000000000000000000000000
χ8744-4-4-44-44000000000004-4-4404i4i−4i−4i−4i−4i4i4i000000000000000000000000000000000000000000000000000000000000000000
χ8844-4-4-44-44000000000004-4-440−4i−4i4i4i4i4i−4i−4i000000000000000000000000000000000000000000000000000000000000000000
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χ914-44-44-4-444-4-440000000000002i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000000000000000000000
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χ934-44-44-4-44-444-40000000000002i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000000000000000000000
χ944-44-44-4-44-444-4000000000000−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000000000000000000000
χ954-4-4-4444-400000004-4-44000002i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000000000000000000
χ964-4-4-4444-400000004-4-4400000−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000000000000000000
χ974-4-4-4444-40000000-444-4000002i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000000000000000000
χ984-4-4-4444-40000000-444-400000−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000000000000000000

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