Finite Group Databasebeta

← Group #134603

Character table — Group #134603

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222224444444444448888888844444444888888888888161616161616161616161616161616164444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ6111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ7111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ8111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ911111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222-2-2-2-22200000000-2-222-2-2-2-200000000000022−2−222−2−222−2−222−2−20000000000000000
χ1922222222222222-2-2-2-22200000000-2-222-2-2-2-2000000000000−2−222−2−222−2−222−2−2220000000000000000
χ20222222222222-2-22222-2-222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-20000000022-2-222-2-2000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ22222222222222-2-2-2-2-2-2-2-20000000022-2-222-2-2000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ2322222222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-22200000000-2-2-2-2222200000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ2522222222-2-2-2-222-2-2-2-22200000000-2-2-2-22222000000000000−2−22222−2−2−2−22222−2−20000000000000000
χ2622222222-2-2-2-2-2-22222-2-222222222-2-22222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-222000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-222000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ29222-2-2-22-200002222-2-2-2-22222-2-2-2-22-200000022-2-2000000000000000000000000002-2002-200000000
χ30222-2-2-22-200002222-2-2-2-22222-2-2-2-22-200000022-2-200000000000000000000000000-2200-2200000000
χ31222-2-2-22-200002222-2-2-2-2-2-2-2-222222-2000000-2-2220000000000000000000000002i−2i002i−2i0000000000
χ32222-2-2-22-200002222-2-2-2-2-2-2-2-222222-2000000-2-222000000000000000000000000−2i2i00−2i2i0000000000
χ33222-2-2-22-20000-2-222-2-2222222-2-2-2-2-22000000-2-2220000000000000000000000002i−2i00−2i2i0000000000
χ34222-2-2-22-20000-2-222-2-2222222-2-2-2-2-22000000-2-222000000000000000000000000−2i2i002i−2i0000000000
χ35222-2-2-22-20000-2-222-2-222-2-2-2-22222-2200000022-2-2000000000000000000000000002-200-2200000000
χ36222-2-2-22-20000-2-222-2-222-2-2-2-22222-2200000022-2-200000000000000000000000000-22002-200000000
χ3722-22-2-2-222i2i−2i−2i2-200002-222−2−222−2−2002i−2i00002−22−2i2i2−i2−i2i2i2−i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ3822-22-2-2-222i2i−2i−2i2-200002-222−2−222−2−2002i−2i00002−22−2i2i2−i2−i2i2i2−i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ3922-22-2-2-222i2i−2i−2i2-200002-2−2−222−2−222002i−2i0000−22−22−i2−i2i2i2−i2−i2i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ4022-22-2-2-222i2i−2i−2i2-200002-2−2−222−2−222002i−2i0000−22−22−i2−i2i2i2−i2−i2i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ4122-22-2-2-222i2i−2i−2i-220000-2222−2−222−2−200−2i2i0000−22−22−i2−i2i2i2i2i2−i2−i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ4222-22-2-2-222i2i−2i−2i-220000-2222−2−222−2−200−2i2i0000−22−22−i2−i2i2i2i2i2−i2−i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ4322-22-2-2-222i2i−2i−2i-220000-22−2−222−2−22200−2i2i00002−22−2i2i2−i2−i2−i2−i2i2i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ4422-22-2-2-222i2i−2i−2i-220000-22−2−222−2−22200−2i2i00002−22−2i2i2−i2−i2−i2−i2i2i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ4522-22-2-2-22−2i−2i2i2i2-200002-222−2−222−2−200−2i2i00002−22−2−i2−i2i2i2−i2−i2i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ4622-22-2-2-22−2i−2i2i2i2-200002-222−2−222−2−200−2i2i00002−22−2−i2−i2i2i2−i2−i2i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ4722-22-2-2-22−2i−2i2i2i2-200002-2−2−222−2−22200−2i2i0000−22−22i2i2−i2−i2i2i2−i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ4822-22-2-2-22−2i−2i2i2i2-200002-2−2−222−2−22200−2i2i0000−22−22i2i2−i2−i2i2i2−i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ4922-22-2-2-22−2i−2i2i2i-220000-2222−2−222−2−2002i−2i0000−22−22i2i2−i2−i2−i2−i2i2i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ5022-22-2-2-22−2i−2i2i2i-220000-2222−2−222−2−2002i−2i0000−22−22i2i2−i2−i2−i2−i2i2i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ5122-22-2-2-22−2i−2i2i2i-220000-22−2−222−2−222002i−2i00002−22−2−i2−i2i2i2i2i2−i2−i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ5222-22-2-2-22−2i−2i2i2i-220000-22−2−222−2−222002i−2i00002−22−2−i2−i2i2i2i2i2−i2−i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ532-2-222-22-22i−2i2i−2i002-22-2002-22-22-22-20000002i−2i000000002i−2i2i−2i000000000000000000000000i2−i22−2i2−i22−2
χ542-2-222-22-22i−2i2i−2i002-22-2002-22-22-22-20000002i−2i000000002i−2i2i−2i000000000000000000000000−i2i2−22−i2i2−22
χ552-2-222-22-22i−2i2i−2i002-22-200-22-22-22-220000002i−2i00000000−2i2i−2i2i0000000000000000000000002−2−i2i2−22i2−i2
χ562-2-222-22-22i−2i2i−2i002-22-200-22-22-22-220000002i−2i00000000−2i2i−2i2i000000000000000000000000−22i2−i22−2−i2i2
χ572-2-222-22-2−2i2i−2i2i002-22-2002-22-22-22-2000000−2i2i00000000−2i2i−2i2i000000000000000000000000i2−i2−22i2−i2−22
χ582-2-222-22-2−2i2i−2i2i002-22-2002-22-22-22-2000000−2i2i00000000−2i2i−2i2i000000000000000000000000−i2i22−2−i2i22−2
χ592-2-222-22-2−2i2i−2i2i002-22-200-22-22-22-22000000−2i2i000000002i−2i2i−2i0000000000000000000000002−2i2−i2−22−i2i2
χ602-2-222-22-2−2i2i−2i2i002-22-200-22-22-22-22000000−2i2i000000002i−2i2i−2i000000000000000000000000−22−i2i22−2i2−i2
χ61444-4-4-44-4000044-4-444-4-400000000-4400000000000000000000000000000000000000000000000000
χ62444-4-4-44-40000-4-4-4-44444000000004-400000000000000000000000000000000000000000000000000
χ6344-4-444-4-400004-40000-442222−22−22−22−2222220000000022−22−22220000000000000000000000000000000000000000
χ6444-4-444-4-400004-40000-44−22−2222222222−22−2200000000−222222−220000000000000000000000000000000000000000
χ6544-4-444-4-40000-4400004-42222−22−22−22−22222200000000−222222−220000000000000000000000000000000000000000
χ6644-4-444-4-40000-4400004-4−22−2222222222−22−220000000022−22−22220000000000000000000000000000000000000000
χ674-444-44-4-44-4-440000000022−22−222222−22−2222000000000000000022−22−222200000000000000000000000000000000
χ684-444-44-4-44-4-4400000000−222222−22−222222−220000000000000000−222222−2200000000000000000000000000000000
χ694-444-44-4-4-444-40000000022−22−222222−22−22220000000000000000−222222−2200000000000000000000000000000000
χ704-444-44-4-4-444-400000000−222222−22−222222−22000000000000000022−22−222200000000000000000000000000000000
χ714-44-44-4-4400000000000022−22−2222−222222−2200004i−4i0000002i2−2i22i2−2i2000000000000000000000000000000000000
χ724-44-44-4-4400000000000022−22−2222−222222−220000−4i4i000000−2i22i2−2i22i2000000000000000000000000000000000000
χ734-44-44-4-44000000000000−222222−2222−22−222200004i−4i000000−2i22i2−2i22i2000000000000000000000000000000000000
χ744-44-44-4-44000000000000−222222−2222−22−22220000−4i4i0000002i2−2i22i2−2i2000000000000000000000000000000000000
χ754-4-444-44-44i−4i4i−4i00-44-440000000000000000−4i4i00000000000000000000000000000000000000000000
χ764-4-444-44-4−4i4i−4i4i00-44-4400000000000000004i−4i00000000000000000000000000000000000000000000
χ774-4-4-4-44440000004-4-44004-44-4-44-440000000000000000000000000000000000000000000000000000
χ784-4-4-4-44440000004-4-4400-44-444-44-40000000000000000000000000000000000000000000000000000
χ794-4-4-4-4444000000-444-400000000000000000000004-4-44000000000000000000000000000000000000
χ804-4-4-4-4444000000-444-40000000000000000000000-444-4000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.