Finite Group Databasebeta

← Group #237992

Character table — Group #237992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122224444888888888888888888881616161611111111222244448888888888888888888816161616
order12224444224444444444444444448888888824882222444422444444444444444444888888882488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222222-2-2-2-222-2-200000000000000000000222222222222-2-2-2-222-2-200000000000000000000
χ10222222222222-2-2-2-2-2-22200000000000000000000222222222222-2-2-2-2-2-22200000000000000000000
χ1122222222-2-2-2-22-22-200000000000000002i2i−2i−2i000022222222-2-2-2-22-22-200000000000000002i2i−2i−2i0000
χ1222222222-2-2-2-22-22-20000000000000000−2i−2i2i2i000022222222-2-2-2-22-22-20000000000000000−2i−2i2i2i0000
χ1322222222-2-2-2-2-22-220000000000002i2i−2i−2i0000000022222222-2-2-2-2-22-220000000000002i2i−2i−2i00000000
χ1422222222-2-2-2-2-22-22000000000000−2i−2i2i2i0000000022222222-2-2-2-2-22-22000000000000−2i−2i2i2i00000000
χ152222-2-2-2-222-2-22-2-220000000022-2-20000000000002222-2-2-2-222-2-22-2-220000000022-2-2000000000000
χ162222-2-2-2-222-2-22-2-2200000000-2-2220000000000002222-2-2-2-222-2-22-2-2200000000-2-222000000000000
χ172222-2-2-2-222-2-2-222-2000022-2-200000000000000002222-2-2-2-222-2-2-222-2000022-2-20000000000000000
χ182222-2-2-2-222-2-2-222-20000-2-22200000000000000002222-2-2-2-222-2-2-222-20000-2-2220000000000000000
χ192222-2-2-2-2-2-22222-2-2000000000000000000002-2002222-2-2-2-2-2-22222-2-2000000000000000000002-200
χ202222-2-2-2-2-2-22222-2-200000000000000000000-22002222-2-2-2-2-2-22222-2-200000000000000000000-2200
χ212222-2-2-2-2-2-222-2-22200000000000000000000002i−2i2222-2-2-2-2-2-222-2-22200000000000000000000002i−2i
χ222222-2-2-2-2-2-222-2-2220000000000000000000000−2i2i2222-2-2-2-2-2-222-2-2220000000000000000000000−2i2i
χ232-2-22-2-2222-22-200002-20000000000i2−i2i2−i2i2−i2i2−i200002-2-22-2-2222-22-200002-20000000000i2−i2i2−i2i2−i2i2−i20000
χ242-2-22-2-2222-22-200002-20000000000−i2i2−i2i2−i2i2−i2i200002-2-22-2-2222-22-200002-20000000000−i2i2−i2i2−i2i2−i2i20000
χ252-2-22-2-2222-22-20000-220000000000i2−i2i2−i2−i2i2−i2i200002-2-22-2-2222-22-20000-220000000000i2−i2i2−i2−i2i2−i2i20000
χ262-2-22-2-2222-22-20000-220000000000−i2i2−i2i2i2−i2i2−i200002-2-22-2-2222-22-20000-220000000000−i2i2−i2i2i2−i2i2−i20000
χ272-2-22-2-222-22-220000002-2000000002−2−222−2−2200002-2-22-2-222-22-220000002-2000000002−2−222−2−220000
χ282-2-22-2-222-22-220000002-200000000−222−2−222−200002-2-22-2-222-22-220000002-200000000−222−2−222−20000
χ292-2-22-2-222-22-22000000-22000000002−2−22−222−200002-2-22-2-222-22-22000000-22000000002−2−22−222−20000
χ302-2-22-2-222-22-22000000-2200000000−222−22−2−2200002-2-22-2-222-22-22000000-2200000000−222−22−2−220000
χ3144-4-44i−4i4i−4i0000000000002-22i−2i000000000000000044-4-44i−4i4i−4i0000000000002-22i−2i0000000000000000
χ3244-4-44i−4i4i−4i000000000000-22−2i2i000000000000000044-4-44i−4i4i−4i000000000000-22−2i2i0000000000000000
χ3344-4-4−4i4i−4i4i0000000000002-2−2i2i000000000000000044-4-4−4i4i−4i4i0000000000002-2−2i2i0000000000000000
χ3444-4-4−4i4i−4i4i000000000000-222i−2i000000000000000044-4-4−4i4i−4i4i000000000000-222i−2i0000000000000000
χ354-44-44i−4i−4i4i00000000000000002-22i−2i0000000000004-44-44i−4i−4i4i00000000000000002-22i−2i000000000000
χ364-44-44i−4i−4i4i0000000000000000-22−2i2i0000000000004-44-44i−4i−4i4i0000000000000000-22−2i2i000000000000
χ374-44-4−4i4i4i−4i00000000000000002-2−2i2i0000000000004-44-4−4i4i4i−4i00000000000000002-2−2i2i000000000000
χ384-44-4−4i4i4i−4i0000000000000000-222i−2i0000000000004-44-4−4i4i4i−4i0000000000000000-222i−2i000000000000
χ394-4-4444-4-44-4-4400000000000000000000000000004-4-4444-4-44-4-440000000000000000000000000000
χ404-4-4444-4-4-444-400000000000000000000000000004-4-4444-4-4-444-40000000000000000000000000000
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ421111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ4311111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ4411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ451111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ461111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ471111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ481111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ49222222222222-2-2-2-222-2-200000000000000000000-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000
χ50222222222222-2-2-2-2-2-22200000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2222222-2-200000000000000000000
χ5122222222-2-2-2-22-22-200000000000000002i2i−2i−2i0000-2-2-2-2-2-2-2-22222-22-220000000000000000−2i−2i2i2i0000
χ5222222222-2-2-2-22-22-20000000000000000−2i−2i2i2i0000-2-2-2-2-2-2-2-22222-22-2200000000000000002i2i−2i−2i0000
χ5322222222-2-2-2-2-22-220000000000002i2i−2i−2i00000000-2-2-2-2-2-2-2-222222-22-2000000000000−2i−2i2i2i00000000
χ5422222222-2-2-2-2-22-22000000000000−2i−2i2i2i00000000-2-2-2-2-2-2-2-222222-22-20000000000002i2i−2i−2i00000000
χ552222-2-2-2-222-2-22-2-220000000022-2-2000000000000-2-2-2-22222-2-222-222-200000000-2-222000000000000
χ562222-2-2-2-222-2-22-2-2200000000-2-222000000000000-2-2-2-22222-2-222-222-20000000022-2-2000000000000
χ572222-2-2-2-222-2-2-222-2000022-2-20000000000000000-2-2-2-22222-2-2222-2-220000-2-2220000000000000000
χ582222-2-2-2-222-2-2-222-20000-2-2220000000000000000-2-2-2-22222-2-2222-2-22000022-2-20000000000000000
χ592222-2-2-2-2-2-22222-2-2000000000000000000002-200-2-2-2-2222222-2-2-2-22200000000000000000000-2200
χ602222-2-2-2-2-2-22222-2-200000000000000000000-2200-2-2-2-2222222-2-2-2-222000000000000000000002-200
χ612222-2-2-2-2-2-222-2-22200000000000000000000002i−2i-2-2-2-2222222-2-222-2-20000000000000000000000−2i2i
χ622222-2-2-2-2-2-222-2-2220000000000000000000000−2i2i-2-2-2-2222222-2-222-2-200000000000000000000002i−2i
χ632-2-22-2-2222-22-200002-20000000000i2−i2i2−i2i2−i2i2−i20000-222-222-2-2-22-220000-220000000000−i2i2−i2i2−i2i2−i2i20000
χ642-2-22-2-2222-22-200002-20000000000−i2i2−i2i2−i2i2−i2i20000-222-222-2-2-22-220000-220000000000i2−i2i2−i2i2−i2i2−i20000
χ652-2-22-2-2222-22-20000-220000000000i2−i2i2−i2−i2i2−i2i20000-222-222-2-2-22-2200002-20000000000−i2i2−i2i2i2−i2i2−i20000
χ662-2-22-2-2222-22-20000-220000000000−i2i2−i2i2i2−i2i2−i20000-222-222-2-2-22-2200002-20000000000i2−i2i2−i2−i2i2−i2i20000
χ672-2-22-2-222-22-220000002-2000000002−2−222−2−220000-222-222-2-22-22-2000000-2200000000−222−2−222−20000
χ682-2-22-2-222-22-220000002-200000000−222−2−222−20000-222-222-2-22-22-2000000-22000000002−2−222−2−220000
χ692-2-22-2-222-22-22000000-22000000002−2−22−222−20000-222-222-2-22-22-20000002-200000000−222−22−2−220000
χ702-2-22-2-222-22-22000000-2200000000−222−22−2−220000-222-222-2-22-22-20000002-2000000002−2−22−222−20000
χ7144-4-44i−4i4i−4i0000000000002-22i−2i0000000000000000-4-444−4i4i−4i4i000000000000-22−2i2i0000000000000000
χ7244-4-44i−4i4i−4i000000000000-22−2i2i0000000000000000-4-444−4i4i−4i4i0000000000002-22i−2i0000000000000000
χ7344-4-4−4i4i−4i4i0000000000002-2−2i2i0000000000000000-4-4444i−4i4i−4i000000000000-222i−2i0000000000000000
χ7444-4-4−4i4i−4i4i000000000000-222i−2i0000000000000000-4-4444i−4i4i−4i0000000000002-2−2i2i0000000000000000
χ754-44-44i−4i−4i4i00000000000000002-22i−2i000000000000-44-44−4i4i4i−4i0000000000000000-22−2i2i000000000000
χ764-44-44i−4i−4i4i0000000000000000-22−2i2i000000000000-44-44−4i4i4i−4i00000000000000002-22i−2i000000000000
χ774-44-4−4i4i4i−4i00000000000000002-2−2i2i000000000000-44-444i−4i−4i4i0000000000000000-222i−2i000000000000
χ784-44-4−4i4i4i−4i0000000000000000-222i−2i000000000000-44-444i−4i−4i4i00000000000000002-2−2i2i000000000000
χ794-4-4444-4-44-4-440000000000000000000000000000-444-4-4-444-444-40000000000000000000000000000
χ804-4-4444-4-4-444-40000000000000000000000000000-444-4-4-4444-4-440000000000000000000000000000

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