Finite Group Databasebeta

← Group #305992

Character table — Group #305992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442222448888888844444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-111-11-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-11-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-11-11111-1-11-1
χ91111111111111111-1-1-1-1111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1111-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111111-1-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-111111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1111-1-1-1-1-1111-1
χ172222222222-22-2-2-222222-2-20000000022-2-200-2-200-2-200000000220000000000000000
χ182222222222-22-2-2-222222-2-200000000-2-2-2-20022002200000000-2-20000000000000000
χ192222222222-22-2-2-22-2-2-2-2-2-200000000222200-2-2002200000000-2-20000000000000000
χ202222222222-22-2-2-22-2-2-2-2-2-200000000-2-222002200-2-200000000220000000000000000
χ2122222222-2-22-2222-20000-2-22222-2-2-2-200002200-2-20000000000000000002-200000000
χ2222222222-2-22-2222-20000-2-22222-2-2-2-20000-2-20022000000000000000000-2200000000
χ2322222222-2-22-2222-20000-2-2-2-2-2-222220000220022000000000000000000-2-200000000
χ2422222222-2-22-2222-20000-2-2-2-2-2-222220000-2-200-2-20000000000000000002200000000
χ25222-22-2-2-2222-2-22-2-222-2-2-2200000000002-20000000022-2-200000022-2-2000000000000
χ26222-22-2-2-2222-2-22-2-222-2-2-2200000000002-200000000-2-222000000-2-222000000000000
χ27222-22-2-2-2222-2-22-2-2-2-222-220000000000-220000000022-2-2000000-2-222000000000000
χ28222-22-2-2-2222-2-22-2-2-2-222-220000000000-2200000000-2-22200000022-2-2000000000000
χ29222-22-2-2-222-2-22-22-222-2-22-222-2-222-2-200-2200000000000022-2-2000000000000000000
χ30222-22-2-2-222-2-22-22-222-2-22-2-2-222-2-22200-22000000000000-2-222000000000000000000
χ31222-22-2-2-222-2-22-22-2-2-2222-222-2-222-2-2002-2000000000000-2-222000000000000000000
χ32222-22-2-2-222-2-22-22-2-2-2222-2-2-222-2-222002-200000000000022-2-2000000000000000000
χ33222-22-2-2-2-2-2-222-2220000-2222-2-2-2-222000000000000000000000000002i−2i002i−2i000000
χ34222-22-2-2-2-2-2-222-2220000-2222-2-2-2-22200000000000000000000000000−2i2i00−2i2i000000
χ35222-22-2-2-2-2-2-222-2220000-22-2-22222-2-2000000000000000000000000002i−2i00−2i2i000000
χ36222-22-2-2-2-2-2-222-2220000-22-2-22222-2-200000000000000000000000000−2i2i002i−2i000000
χ3722-22-22-2-22-20-200022-22-2002−22−22−22−20000002i−2i002i−2ii2−i2i2−i22−22−200i2−i2i2−i2000000000000
χ3822-22-22-2-22-20-200022-22-2002−22−22−22−2000000−2i2i00−2i2i−i2i2−i2i22−22−200−i2i2−i2i2000000000000
χ3922-22-22-2-22-20-200022-22-200−22−22−22−220000002i−2i002i−2i−i2i2−i2i2−22−2200−i2i2−i2i2000000000000
χ4022-22-22-2-22-20-200022-22-200−22−22−22−22000000−2i2i00−2i2ii2−i2i2−i2−22−2200i2−i2i2−i2000000000000
χ4122-22-22-2-22-20-20002-22-22002−22−22−22−20000002i−2i00−2i2ii2−i2i2−i2−22−2200−i2i2−i2i2000000000000
χ4222-22-22-2-22-20-20002-22-22002−22−22−22−2000000−2i2i002i−2i−i2i2−i2i2−22−2200i2−i2i2−i2000000000000
χ4322-22-22-2-22-20-20002-22-2200−22−22−22−220000002i−2i00−2i2i−i2i2−i2i22−22−200i2−i2i2−i2000000000000
χ4422-22-22-2-22-20-20002-22-2200−22−22−22−22000000−2i2i002i−2ii2−i2i2−i22−22−200−i2i2−i2i2000000000000
χ4522-2-2-2-2222-202000-22-2-22002−2−222−2−222i−2i0000000000i2−i2−i2i22−2−222i−2ii2−i2−i2i2000000000000
χ4622-2-2-2-2222-202000-22-2-22002−2−222−2−22−2i2i0000000000−i2i2i2−i22−2−22−2i2i−i2i2i2−i2000000000000
χ4722-2-2-2-2222-202000-22-2-2200−222−2−222−22i−2i0000000000−i2i2i2−i2−222−22i−2i−i2i2i2−i2000000000000
χ4822-2-2-2-2222-202000-22-2-2200−222−2−222−2−2i2i0000000000i2−i2−i2i2−222−2−2i2ii2−i2−i2i2000000000000
χ4922-2-2-2-2222-202000-2-222-2002−2−222−2−222i−2i0000000000i2−i2−i2i2−222−2−2i2i−i2i2i2−i2000000000000
χ5022-2-2-2-2222-202000-2-222-2002−2−222−2−22−2i2i0000000000−i2i2i2−i2−222−22i−2ii2−i2−i2i2000000000000
χ5122-2-2-2-2222-202000-2-222-200−222−2−222−22i−2i0000000000−i2i2i2−i22−2−22−2i2ii2−i2−i2i2000000000000
χ5222-2-2-2-2222-202000-2-222-200−222−2−222−2−2i2i0000000000i2−i2−i2i22−2−222i−2i−i2i2i2−i2000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-44-4-4-4-4-444-44-4400004-40000000000000000000000000000000000000000000000
χ5544-44-44-4-4-4404000-400000022−2222−22−2222−222200000000000000000000000000000000000000
χ5644-44-44-4-4-4404000-4000000−2222−222222−2222−2200000000000000000000000000000000000000
χ5744-4-4-4-444-440-4000400000022−22−2222−222222−2200000000000000000000000000000000000000
χ5844-4-4-4-444-440-40004000000−222222−2222−22−222200000000000000000000000000000000000000
χ594-4-444-4-440040-4-44000000000000000000000000000000000000000000000002i2−2i20000
χ604-4-444-4-440040-4-4400000000000000000000000000000000000000000000000−2i22i20000
χ614-4-444-4-4400-4044-400000000000000000004i−4i00000000000000000000000000000000
χ624-4-444-4-4400-4044-40000000000000000000−4i4i00000000000000000000000000000000
χ634-4-4-4444-400404-4-4000000000000000000000004i−4i0000000000000000000000000000
χ644-4-4-4444-400404-4-400000000000000000000000−4i4i0000000000000000000000000000
χ654-4-4-4444-400-40-444000000000000000000000000000000000000000000000000022−2200
χ664-4-4-4444-400-40-4440000000000000000000000000000000000000000000000000−222200
χ678-888-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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