Finite Group Databasebeta

← Group #325261

Character table — Group #325261

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444444444888844448888888888888888888888888844884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ10111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-11-11
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111111111-1-11-1-11
χ17222222222-2-2-2222-2-2-22222-2-2-2-2000022-2-2000000000000000000000000002-2000000
χ18222222222-2-2-2222-2-2-22222-2-2-2-20000-2-22200000000000000000000000000-22000000
χ19222222222-2-2-2222-2-2-2-2-2-2-22222000022-2-200000000000000000000000000-22000000
χ20222222222-2-2-2222-2-2-2-2-2-2-222220000-2-222000000000000000000000000002-2000000
χ2122222222-2222-2-2-22-2-222-2-222-2-222220000-2-2-2-2000000000000000022000000000000
χ2222222222-2222-2-2-22-2-222-2-222-2-2-2-2-2-2000022220000000000000000-2-2000000000000
χ2322222222-2222-2-2-22-2-2-2-222-2-22222220000-2-2220000000000000000-2-2000000000000
χ2422222222-2222-2-2-22-2-2-2-222-2-222-2-2-2-2000022-2-2000000000000000022000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-2220000000000000000000000000000002i2i−2i−2i002i−2i0000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000000000−2i−2i2i2i00−2i2i0000
χ2722222222-2-2-2-2-2-2-2-222-2-22222-2-20000000000000000000000000000002i2i−2i−2i00−2i2i0000
χ2822222222-2-2-2-2-2-2-2-222-2-22222-2-2000000000000000000000000000000−2i−2i2i2i002i−2i0000
χ292222-2-2-2-2222-2-2-22-22-20000000022-2-200002-2000000000022-2-222-2-200000000000000
χ302222-2-2-2-2222-2-2-22-22-20000000022-2-200002-20000000000-2-222-2-22200000000000000
χ312222-2-2-2-2222-2-2-22-22-200000000-2-2220000-22000000000022-2-2-2-22200000000000000
χ322222-2-2-2-2222-2-2-22-22-200000000-2-2220000-220000000000-2-22222-2-200000000000000
χ332222-2-2-2-2-222-222-2-2-220000000022-2-20000-220022-2-222-2-20000000000000000000000
χ342222-2-2-2-2-222-222-2-2-220000000022-2-20000-2200-2-222-2-2220000000000000000000000
χ352222-2-2-2-2-222-222-2-2-2200000000-2-22200002-20022-2-2-2-2220000000000000000000000
χ362222-2-2-2-2-222-222-2-2-2200000000-2-22200002-200-2-22222-2-20000000000000000000000
χ3722-2-222-2-202-2-20002002-2002-2002-22-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-2000000000000
χ3822-2-222-2-202-2-20002002-2002-2002-22-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-2000000000000
χ3922-2-222-2-202-2-20002002-2002-200-22-2200000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2-22000000000000
χ4022-2-222-2-202-2-20002002-2002-200-22-2200000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2-22000000000000
χ4122-2-222-2-202-2-2000200-2200-22002-22-200000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2-22000000000000
χ4222-2-222-2-202-2-2000200-2200-22002-22-200000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2-22000000000000
χ4322-2-222-2-202-2-2000200-2200-2200-22-2200000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i22-2000000000000
χ4422-2-222-2-202-2-2000200-2200-2200-22-2200000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i22-2000000000000
χ4522-2-2-2-22202-22000-200002-2002-22-2-220000002-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000
χ4622-2-2-2-22202-22000-200002-2002-22-2-220000002-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000000000
χ4722-2-2-2-22202-22000-200002-2002-2-222-2000000-22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000000000
χ4822-2-2-2-22202-22000-200002-2002-2-222-2000000-22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000000000
χ4922-2-2-2-22202-22000-20000-2200-222-2-22000000-22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000000000
χ5022-2-2-2-22202-22000-20000-2200-222-2-22000000-22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000000000
χ5122-2-2-2-22202-22000-20000-2200-22-222-20000002-2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000000000
χ5222-2-2-2-22202-22000-20000-2200-22-222-20000002-2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000000000
χ534444-4-4-4-44-4-44-4-444-4400000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-4-4444-444-400000000000000000000000000000000000000000000000000
χ5544-4-444-4-40-444000-4004-400-4400000000000000000000000000000000000000000000
χ5644-4-444-4-40-444000-400-44004-400000000000000000000000000000000000000000000
χ5744-4-4-4-4440-44-4000400004-400-44000000000000000000000000000000000000000000
χ5844-4-4-4-4440-44-400040000-44004-4000000000000000000000000000000000000000000
χ594-44-44-44-440004-4-40000000000000000000000000000000000000000022−2222−2200000000
χ604-44-44-44-440004-4-400000000000000000000000000000000000000000−2222−222200000000
χ614-44-44-44-4-4000-444000000000000000000000000000000000000000002i2−2i2−2i22i200000000
χ624-44-44-44-4-4000-44400000000000000000000000000000000000000000−2i22i22i2−2i200000000
χ634-44-4-44-444000-44-40000000000000004i−4i000000000000000000000000000000000000
χ644-44-4-44-444000-44-4000000000000000−4i4i000000000000000000000000000000000000
χ654-44-4-44-44-40004-44000000000000000004-40000000000000000000000000000000000
χ664-44-4-44-44-40004-4400000000000000000-440000000000000000000000000000000000
χ678-8-888-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-88-888-8000000000000000000000000000000000000000000000000000000000000

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