Finite Group Databasebeta

← Group #265232

Character table — Group #265232

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222224444444444444444444444444488888888888888161616161616161632323232
order12222222224444888888882244444444444488888888888844444488888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-111-1-1
χ61111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-111
χ71111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1111-1-1-1-1-111
χ81111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1-111111-1-1
χ911111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-11-1-11-11-1
χ1011111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-111-11-11
χ1111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1111-1-11-1-1-11-11
χ1211111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-111-1111-11-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1111-1-11
χ1411111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111111-11-1-1-111-111-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-11-1111-1-11-1-11
χ172222222222-2-2-2-20000000022-2-2222222-2-2-2-2000000000000-2-222-2-200000000000000000000
χ182222222222-2-2-2-20000000022-2-222-2-2-2-22222000000000000-2-2-2-22200000000000000000000
χ192222222222-2-2-2-200000000-2-2-2-2-2-22222-2-2-2-200000000000022-2-22200000000000000000000
χ202222222222-2-2-2-200000000-2-2-2-2-2-2-2-2-2-222220000000000002222-2-200000000000000000000
χ21222222-2-2-2-222222222222222-2-2-2-200000000-2-2-2-2000000002-20000000022-2-2000000000000
χ22222222-2-2-2-2222222222222-2-2-2-22200000000-2-2-2-200000000-2200000000-2-222000000000000
χ23222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-2000000002222000000002-200000000-2-222000000000000
χ24222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22200000000222200000000-220000000022-2-2000000000000
χ25222222-2-2-2-2-2-2-2-2000000002222-2-20000000000002i2i2i2i−2i−2i−2i−2i-2200002i2i−2i−2i0000000000000000
χ26222222-2-2-2-2-2-2-2-2000000002222-2-2000000000000−2i−2i−2i−2i2i2i2i2i-220000−2i−2i2i2i0000000000000000
χ27222222-2-2-2-2-2-2-2-200000000-2-222220000000000002i2i2i2i−2i−2i−2i−2i2-20000−2i−2i2i2i0000000000000000
χ28222222-2-2-2-2-2-2-2-200000000-2-22222000000000000−2i−2i−2i−2i2i2i2i2i2-200002i2i−2i−2i0000000000000000
χ292222-2-222-2-2-2-2222222-2-2-2-2002-2000000000022-2-2000000000000000000000002000-22-20000
χ302222-2-222-2-2-2-2222222-2-2-2-2002-2000000000022-2-200000000000000000000000-20002-220000
χ312222-2-222-2-2-2-222-2-2-2-22222002-20000000000-2-222000000000000000000000002000-2-220000
χ322222-2-222-2-2-2-222-2-2-2-22222002-20000000000-2-22200000000000000000000000-200022-20000
χ332222-2-2-2-222-2-2222222-2-2-2-200-220000000000-2-222000000000000000000000020-22-20000000
χ342222-2-2-2-222-2-2222222-2-2-2-200-220000000000-2-2220000000000000000000000-202-220000000
χ352222-2-2-2-222-2-222-2-2-2-2222200-22000000000022-2-2000000000000000000000020-2-220000000
χ362222-2-2-2-222-2-222-2-2-2-2222200-22000000000022-2-20000000000000000000000-2022-20000000
χ3722-2-22-22-22-20000i2i2−i2−i2i2i2−i2−i22-2002-200002i2i−2i−2ii2−i2i2−i222−2−222−2−200002i−2i2−22−2i2−i2i2−i2000000000000
χ3822-2-22-22-22-20000i2i2−i2−i2i2i2−i2−i22-2002-20000−2i−2i2i2ii2−i2i2−i2−2−222−2−2220000−2i2i−22−22i2−i2i2−i2000000000000
χ3922-2-22-22-22-20000i2i2−i2−i2i2i2−i2−i2-2200-2200002i2i−2i−2ii2−i2i2−i222−2−222−2−20000−2i2i−22−22−i2i2−i2i2000000000000
χ4022-2-22-22-22-20000i2i2−i2−i2i2i2−i2−i2-2200-220000−2i−2i2i2ii2−i2i2−i2−2−222−2−22200002i−2i2−22−2−i2i2−i2i2000000000000
χ4122-2-22-22-22-20000−i2−i2i2i2−i2−i2i2i22-2002-200002i2i−2i−2i−i2i2−i2i2−2−222−2−22200002i−2i−22−22−i2i2−i2i2000000000000
χ4222-2-22-22-22-20000−i2−i2i2i2−i2−i2i2i22-2002-20000−2i−2i2i2i−i2i2−i2i222−2−222−2−20000−2i2i2−22−2−i2i2−i2i2000000000000
χ4322-2-22-22-22-20000−i2−i2i2i2−i2−i2i2i2-2200-2200002i2i−2i−2i−i2i2−i2i2−2−222−2−2220000−2i2i2−22−2i2−i2i2−i2000000000000
χ4422-2-22-22-22-20000−i2−i2i2i2−i2−i2i2i2-2200-220000−2i−2i2i2i−i2i2−i2i222−2−222−2−200002i−2i−22−22i2−i2i2−i2000000000000
χ4522-2-22-2-22-220000i2i2−i2−i2i2i2−i2−i22-200-2222-2-20000−i2i2−i2i2i2i2−i2−i2−i2−i2i2i2002-200i2−i2−i2i2i2−i2−i2i2000000000000
χ4622-2-22-2-22-220000i2i2−i2−i2i2i2−i2−i22-200-22-2-2220000−i2i2−i2i2−i2−i2i2i2i2i2−i2−i200-2200−i2i2i2−i2i2−i2−i2i2000000000000
χ4722-2-22-2-22-220000i2i2−i2−i2i2i2−i2−i2-22002-222-2-20000−i2i2−i2i2i2i2−i2−i2−i2−i2i2i200-2200−i2i2i2−i2−i2i2i2−i2000000000000
χ4822-2-22-2-22-220000i2i2−i2−i2i2i2−i2−i2-22002-2-2-2220000−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2002-200i2−i2−i2i2−i2i2i2−i2000000000000
χ4922-2-22-2-22-220000−i2−i2i2i2−i2−i2i2i22-200-2222-2-20000i2−i2i2−i2−i2−i2i2i2i2i2−i2−i2002-200−i2i2i2−i2−i2i2i2−i2000000000000
χ5022-2-22-2-22-220000−i2−i2i2i2−i2−i2i2i22-200-22-2-2220000i2−i2i2−i2i2i2−i2−i2−i2−i2i2i200-2200i2−i2−i2i2−i2i2i2−i2000000000000
χ5122-2-22-2-22-220000−i2−i2i2i2−i2−i2i2i2-22002-222-2-20000i2−i2i2−i2−i2−i2i2i2i2i2−i2−i200-2200i2−i2−i2i2i2−i2−i2i2000000000000
χ5222-2-22-2-22-220000−i2−i2i2i2−i2−i2i2i2-22002-2-2-2220000i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2002-200−i2i2i2−i2i2−i2−i2i2000000000000
χ534444-4-444-4-444-4-40000000000-44000000000000000000000000000000000000000000000000
χ544444-4-4-4-44444-4-400000000004-4000000000000000000000000000000000000000000000000
χ5544-4-4-444-4-4400002i22i2−2i2−2i2−2i2−2i22i22i2000000000000002i2−2i2−2i22i20000000000000000000000000000000000
χ5644-4-4-444-4-440000−2i2−2i22i22i22i22i2−2i2−2i200000000000000−2i22i22i2−2i20000000000000000000000000000000000
χ5744-4-4-44-444-400002i22i2−2i2−2i2−2i2−2i22i22i200000000000000−2i22i22i2−2i20000000000000000000000000000000000
χ5844-4-4-44-444-40000−2i2−2i22i22i22i22i2−2i2−2i2000000000000002i2−2i2−2i22i20000000000000000000000000000000000
χ594-44-4000000004-400004-44-40000002i−2i2i−2i2i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ604-44-4000000004-400004-44-4000000−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ614-44-4000000004-40000-44-440000002i−2i2i−2i2i−2i2i−2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ624-44-4000000004-40000-44-44000000−2i2i−2i2i−2i2i−2i2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ634-44-400000000-444i−4i4i−4i00000000002i−2i2i−2i−2i2i−2i2i00002-22-2-22-2200000000000000000000000000
χ644-44-400000000-444i−4i4i−4i0000000000−2i2i−2i2i2i−2i2i−2i0000-22-222-22-200000000000000000000000000
χ654-44-400000000-44−4i4i−4i4i00000000002i−2i2i−2i−2i2i−2i2i0000-22-222-22-200000000000000000000000000
χ664-44-400000000-44−4i4i−4i4i0000000000−2i2i−2i2i2i−2i2i−2i00002-22-2-22-2200000000000000000000000000
χ674-4-440000004i−4i0022−22−22222i2−2i2−2i22i20000002i−2i−2i2i2-2-220000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000
χ684-4-440000004i−4i0022−22−22222i2−2i2−2i22i2000000−2i2i2i−2i-222-200002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000
χ694-4-440000004i−4i00−222222−22−2i22i22i2−2i20000002i−2i−2i2i2-2-2200002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000
χ704-4-440000004i−4i00−222222−22−2i22i22i2−2i2000000−2i2i2i−2i-222-20000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000
χ714-4-44000000−4i4i0022−22−2222−2i22i22i2−2i20000002i−2i−2i2i-222-20000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000
χ724-4-44000000−4i4i0022−22−2222−2i22i22i2−2i2000000−2i2i2i−2i2-2-2200002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000
χ734-4-44000000−4i4i00−222222−222i2−2i2−2i22i20000002i−2i−2i2i-222-200002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000
χ744-4-44000000−4i4i00−222222−222i2−2i2−2i22i2000000−2i2i2i−2i2-2-220000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.