Finite Group Databasebeta

← Group #101006

Character table — Group #101006

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444422444488888888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222222222-2-22222222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-222-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000
χ2122222222-2-2-2-222222-20000-2-200002-2002-2000000000022-2-222-2-20000000000000000
χ2222222222-2-2-2-222222-20000-2-200002-2002-20000000000-2-222-2-2220000000000000000
χ2322222222-2-2-2-22222-220000-2-20000-2200-220022-2-222-2-2000000000000000000000000
χ2422222222-2-2-2-22222-220000-2-20000-2200-2200-2-222-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22-200002200002-200-22002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22-200002200002-200-2200−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-220000220000-22002-200000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-220000220000-22002-20000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-2-2-22-22-2-2222-2-2002i2i−2i−2i2-22i2i−2i−2i00000000000000000000000000000000i2−i2i2−i22−22−2
χ30222-2-2-22-22-2-2222-2-2002i2i−2i−2i2-22i2i−2i−2i00000000000000000000000000000000−i2i2−i2i2−22−22
χ31222-2-2-22-22-2-2222-2-200−2i−2i2i2i2-2−2i−2i2i2i00000000000000000000000000000000i2−i2i2−i2−22−22
χ32222-2-2-22-22-2-2222-2-200−2i−2i2i2i2-2−2i−2i2i2i00000000000000000000000000000000−i2i2−i2i22−22−2
χ33222-2-2-22-22-2-22-2-222002i2i−2i−2i-22−2i−2i2i2i000000000000000000000000000000002−2−22−i2i2i2−i2
χ34222-2-2-22-22-2-22-2-222002i2i−2i−2i-22−2i−2i2i2i00000000000000000000000000000000−222−2i2−i2−i2i2
χ35222-2-2-22-22-2-22-2-22200−2i−2i2i2i-222i2i−2i−2i000000000000000000000000000000002−2−22i2−i2−i2i2
χ36222-2-2-22-22-2-22-2-22200−2i−2i2i2i-222i2i−2i−2i00000000000000000000000000000000−222−2−i2i2i2−i2
χ3722-222-2-2-222-2-20000222-22-2000000-2-22-200002−22−22−22−22−22−22−22−20000000000000000
χ3822-222-2-2-222-2-20000222-22-2000000-2-22-20000−22−22−22−22−22−22−22−220000000000000000
χ3922-222-2-2-222-2-2000022-22-22000000-2-2-2200002−22−22−22−2−22−22−22−220000000000000000
χ4022-222-2-2-222-2-2000022-22-22000000-2-2-220000−22−22−22−222−22−22−22−20000000000000000
χ4122-222-2-2-222-2-20000-2-22-22-200000022-220000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ4222-222-2-2-222-2-20000-2-22-22-200000022-220000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ4322-222-2-2-222-2-20000-2-2-22-22000000222-20000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ4422-222-2-2-222-2-20000-2-2-22-22000000222-20000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ4522-222-2-2-2-2-22200002-20000002i−2i2i−2i-2200002i−2ii2−i2−i2i2−i2i2i2−i22−2−222−2−220000000000000000
χ4622-222-2-2-2-2-22200002-20000002i−2i2i−2i-2200002i−2i−i2i2i2−i2i2−i2−i2i2−222−2−222−20000000000000000
χ4722-222-2-2-2-2-22200002-2000000−2i2i−2i2i-220000−2i2ii2−i2−i2i2−i2i2i2−i2−222−2−222−20000000000000000
χ4822-222-2-2-2-2-22200002-2000000−2i2i−2i2i-220000−2i2i−i2i2i2−i2i2−i2−i2i22−2−222−2−220000000000000000
χ4922-222-2-2-2-2-2220000-220000002i−2i2i−2i2-20000−2i2i2−2−222−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ5022-222-2-2-2-2-2220000-220000002i−2i2i−2i2-20000−2i2i−222−2−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ5122-222-2-2-2-2-2220000-22000000−2i2i−2i2i2-200002i−2i2−2−222−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ5222-222-2-2-2-2-2220000-22000000−2i2i−2i2i2-200002i−2i−222−2−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ53444-4-4-44-4-444-444-4-4000000-4400000000000000000000000000000000000000000000
χ54444-4-4-44-4-444-4-4-4440000004-400000000000000000000000000000000000000000000
χ5544-4-4-44-444-44-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ5644-4-4-44-444-44-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ5744-4-4-44-44-44-440000000000004-4-440000000000000000000000000000000000000000
χ5844-4-4-44-44-44-44000000000000-444-40000000000000000000000000000000000000000
χ594-4-44-444-400004-44-40000000000000000000000000000000000002i−2i2i−2i000000000000
χ604-4-44-444-400004-44-4000000000000000000000000000000000000−2i2i−2i2i000000000000
χ614-4-44-444-40000-44-440000000000000000000000000000000000002i−2i−2i2i000000000000
χ624-4-44-444-40000-44-44000000000000000000000000000000000000−2i2i2i−2i000000000000
χ634-4-4-44-44400004-4-4400000000000000000000000000000000000000002-22-200000000
χ644-4-4-44-44400004-4-440000000000000000000000000000000000000000-22-2200000000
χ654-4-4-44-4440000-444-400000000000000000000000000000000000000002-2-2200000000
χ664-4-4-44-4440000-444-40000000000000000000000000000000000000000-222-200000000
χ678-888-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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