Finite Group Databasebeta

← Group #400697

Character table — Group #400697

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222444444444444888888888888888888888816161616161616161616161616161616
order12442222222444444444448888888822224444448888888888882444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1
χ9111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ10111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ11111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111
χ12111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-11111-1-1-1-111
χ17222222-2-2-22-222-22-2-2-200002i2i2i2i−2i−2i−2i−2i000000000000000000000000000000002i−2i002-2
χ18222222-2-2-22-222-22-2-2-200002i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000−2i2i00-22
χ19222222-2-2-22-222-22-2-2-20000−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000002i−2i00-22
χ20222222-2-2-22-222-22-2-2-20000−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000−2i2i002-2
χ2122222-22-2-2-222-22-22-2-2000000000000000000000022-2-22i2i−2i−2i2i2i−2i−2i0000000000000000
χ2222222-22-2-2-222-22-22-2-2000000000000000000000022-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222-22-2-2-222-22-22-2-20000000000000000000000-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000
χ2422222-22-2-2-222-22-22-2-20000000000000000000000-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000
χ252222-22-22-2-22-2-2-2222-20000000000002-22-22-22-2002-22-2000000000000000000000000
χ262222-22-22-2-22-2-2-2222-20000000000002-2-222-2-2200-22-22000000000000000000000000
χ272222-22-22-2-22-2-2-2222-2000000000000-222-2-222-200-22-22000000000000000000000000
χ282222-22-22-2-22-2-2-2222-2000000000000-22-22-22-22002-22-2000000000000000000000000
χ292222-2-222-22-2-222-2-22-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000002-2002i−2i00
χ302222-2-222-22-2-222-2-22-200002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000-2200−2i2i00
χ312222-2-222-22-2-222-2-22-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000002-200−2i2i00
χ322222-2-222-22-2-222-2-22-20000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000-22002i−2i00
χ332222-2-2-2-2222-22-2-22-22222222-2-2-2-22200000000-2-22-2-22000000000000000000000000
χ342222-2-2-2-2222-22-2-22-222222-2-22222-2-200000000-2-2-222-2000000000000000000000000
χ352222-2-2-2-2222-22-2-22-22-2-2-2-222-2-2-2-2220000000022-222-2000000000000000000000000
χ362222-2-2-2-2222-22-2-22-22-2-2-2-2-2-22222-2-200000000222-2-22000000000000000000000000
χ3722-2-222-2-2-22-2-2-22-222222-2-2000000002-200-22002-200002-22-200000000000000000000
χ3822-2-222-2-2-22-2-2-22-222222-2-200000000-22002-2002-20000-22-2200000000000000000000
χ3922-2-222-2-2-22-2-2-22-2222-2-222000000002-200-2200-220000-22-2200000000000000000000
χ4022-2-222-2-2-22-2-2-22-2222-2-22200000000-22002-200-2200002-22-200000000000000000000
χ4122-2-22-22-2-2-22-22-22-22200002-22-22-22-200000000000000000000002-22-2000000000000
χ4222-2-22-22-2-2-22-22-22-22200002-22-22-22-20000000000000000000000-22-22000000000000
χ4322-2-22-22-2-2-22-22-22-2220000-22-22-22-2200000000000000000000002-2-22000000000000
χ4422-2-22-22-2-2-22-22-22-2220000-22-22-22-220000000000000000000000-222-2000000000000
χ4522-2-22-2-222-2-2-22222-2-200002i−2i2i−2i−2i2i−2i2i002200-2-20000002i−2i−2i2i00000000000000000000
χ4622-2-22-2-222-2-2-22222-2-200002i−2i2i−2i−2i2i−2i2i00-2-20022000000−2i2i2i−2i00000000000000000000
χ4722-2-22-2-222-2-2-22222-2-20000−2i2i−2i2i2i−2i2i−2i002200-2-2000000−2i2i2i−2i00000000000000000000
χ4822-2-22-2-222-2-2-22222-2-20000−2i2i−2i2i2i−2i2i−2i00-2-200220000002i−2i−2i2i00000000000000000000
χ4922-2-2-222-22-2-222-2-222-200002i−2i−2i2i2i−2i−2i2i2200-2-20000000000002i−2i2i−2i0000000000000000
χ5022-2-2-222-22-2-222-2-222-200002i−2i−2i2i2i−2i−2i2i-2-20022000000000000−2i2i−2i2i0000000000000000
χ5122-2-2-222-22-2-222-2-222-20000−2i2i2i−2i−2i2i2i−2i2200-2-2000000000000−2i2i−2i2i0000000000000000
χ5222-2-2-222-22-2-222-2-222-20000−2i2i2i−2i−2i2i2i−2i-2-200220000000000002i−2i2i−2i0000000000000000
χ5322-2-2-22-22-2-22222-2-2-2200002-2-22-222-2000000000000000000000000002i−2i2i−2i00000000
χ5422-2-2-22-22-2-22222-2-2-2200002-2-22-222-200000000000000000000000000−2i2i−2i2i00000000
χ5522-2-2-22-22-2-22222-2-2-220000-222-22-2-22000000000000000000000000002i−2i−2i2i00000000
χ5622-2-2-22-22-2-22222-2-2-220000-222-22-2-2200000000000000000000000000−2i2i2i−2i00000000
χ5722-2-2-2-222-22-22-2-222-2222-2-200000000002-200-22-22000000002-2-220000000000000000
χ5822-2-2-2-222-22-22-2-222-2222-2-20000000000-22002-2-2200000000-222-20000000000000000
χ5922-2-2-2-222-22-22-2-222-22-2-22200000000002-200-222-200000000-222-20000000000000000
χ6022-2-2-2-222-22-22-2-222-22-2-2220000000000-22002-22-2000000002-2-220000000000000000
χ6144444-4-444-4-44-4-4-4-44400000000000000000000000000000000000000000000000000
χ624444-444-44-4-4-4-444-4-4400000000000000000000000000000000000000000000000000
χ6344-4-44444444-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000
χ6444-4-4-4-4-4-44444-444-44-400000000000000000000000000000000000000000000000000
χ658-88i−8i000000000000004-44i−4i0000000000000000000000000000000000000000000000
χ668-88i−8i00000000000000-44−4i4i0000000000000000000000000000000000000000000000
χ678-8−8i8i000000000000004-4−4i4i0000000000000000000000000000000000000000000000
χ688-8−8i8i00000000000000-444i−4i0000000000000000000000000000000000000000000000

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