Finite Group Databasebeta

← Group #305698

Character table — Group #305698

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-111111111111111-1-1-1-1-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1111-1-111-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111
χ71111111111111111111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1
χ91111111111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-11
χ101111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1111111-1-11-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1111111-1111-1-1-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-111-1-1-11111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11-1-1111-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1111-1-1-11111-1-111-1
χ172222222222-2-22-22-20000-2-2222222220000-2-200-2-2000000000000-2000000000000
χ182222222222-2-22-22-20000-2-22222-2-2-2-200002200-2-20000000000002000000000000
χ192222222222-2-22-22-20000-2-2-2-2-2-222-2-20000-2-200220000000000002000000000000
χ202222222222-2-22-22-20000-2-2-2-2-2-2-2-2220000220022000000000000-2000000000000
χ2122222222-2-222-22-222222-2-20000000022-2-20022000000-2-2000000000-2000000000
χ2222222222-2-222-22-222222-2-200000000-2-2-2-200-2-2000000220000000002000000000
χ2322222222-2-222-22-22-2-2-2-2-2-200000000222200-2-200000022000000000-2000000000
χ2422222222-2-222-22-22-2-2-2-2-2-200000000-2-2220022000000-2-20000000002000000000
χ25222-2-2-2-222222-2-2-2-222-2-22-200002-200002-22-2000000000000000000002-20000000
χ26222-2-2-2-222222-2-2-2-222-2-22-20000-2200002-2-2200000000000000000000-220000000
χ27222-2-2-2-222222-2-2-2-2-2-2222-200002-20000-222-200000000000000000000-220000000
χ28222-2-2-2-222222-2-2-2-2-2-2222-20000-220000-22-22000000000000000000002-20000000
χ29222-2-2-2-2222-2-2-22-220000-2200002-2000000-2200002i2i−2i−2i0000000002i−2i0000000000
χ30222-2-2-2-2222-2-2-22-220000-2200002-2000000-220000−2i−2i2i2i000000000−2i2i0000000000
χ31222-2-2-2-2222-2-2-22-220000-220000-220000002-200002i2i−2i−2i000000000−2i2i0000000000
χ32222-2-2-2-2222-2-2-22-220000-220000-220000002-20000−2i−2i2i2i0000000002i−2i0000000000
χ33222-2-2-2-22-2-2222-22-222-2-2-220000000000-2200000000000000002i−2i000000002i−2i000
χ34222-2-2-2-22-2-2222-22-222-2-2-220000000000-220000000000000000−2i2i00000000−2i2i000
χ35222-2-2-2-22-2-2222-22-2-2-222-2200000000002-200000000000000002i−2i00000000−2i2i000
χ36222-2-2-2-22-2-2222-22-2-2-222-2200000000002-20000000000000000−2i2i000000002i−2i000
χ3722-22-22-2-2002-20-2022-22-20022−2−200002i−2i00002i−2i2−22−22−200i2i2−i2−i200000000i2−i200000
χ3822-22-22-2-2002-20-2022-22-20022−2−20000−2i2i0000−2i2i2−22−22−200−i2−i2i2i200000000−i2i200000
χ3922-22-22-2-2002-20-2022-22-200−2−22200002i−2i00002i−2i−22−22−2200−i2−i2i2i200000000−i2i200000
χ4022-22-22-2-2002-20-2022-22-200−2−2220000−2i2i0000−2i2i−22−22−2200i2i2−i2−i200000000i2−i200000
χ4122-22-22-2-2002-20-202-22-220022−2−200002i−2i0000−2i2i2−2−22−2200−i2−i2i2i200000000i2−i200000
χ4222-22-22-2-2002-20-202-22-220022−2−20000−2i2i00002i−2i2−2−22−2200i2i2−i2−i200000000−i2i200000
χ4322-22-22-2-2002-20-202-22-2200−2−22200002i−2i0000−2i2i−222−22−200i2i2−i2−i200000000−i2i200000
χ4422-22-22-2-2002-20-202-22-2200−2−2220000−2i2i00002i−2i−222−22−200−i2−i2i2i200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-4-44-4-4-4-4444400004-40000000000000000000000000000000000000000000
χ4744-44-44-4-400-44040-40000002222−22−22000000000000−22220000000000000000000000000
χ4844-44-44-4-400-44040-4000000−22−22222200000000000022−220000000000000000000000000
χ4944-4-44-44-4004-4040-44-4-44000000000000000000000000000000000000000000000
χ5044-4-44-44-4004-4040-4-444-4000000000000000000000000000000000000000000000
χ5144-4-44-44-400-440-4040000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5244-4-44-44-400-440-404000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ534-444-4-44-44-40040-4000000000000000000000000000000022−2222−22000000000000000
χ544-444-4-44-44-40040-40000000000000000000000000000000−2222−2222000000000000000
χ554-444-4-44-4-4400-40400000004i−4i4i−4i000000000000000000000000000000000000000
χ564-444-4-44-4-4400-4040000000−4i4i−4i4i000000000000000000000000000000000000000
χ574-44-444-4-44-400-404000000000000000000000000000000000000000000000002i2−2i20
χ584-44-444-4-44-400-40400000000000000000000000000000000000000000000000−2i22i20
χ594-44-444-4-4-440040-400000000000004-400000000000000000000000000000000000
χ604-44-444-4-4-440040-40000000000000-4400000000000000000000000000000000000
χ614-4-444-4-44000000000000002i2−2i2−2i22i200000000000000000022−222i−2i−2i2i000000000000000
χ624-4-444-4-44000000000000002i2−2i2−2i22i2000000000000000000−2222−2i2i2i−2i000000000000000
χ634-4-444-4-4400000000000000−2i22i22i2−2i200000000000000000022−22−2i2i2i−2i000000000000000
χ644-4-444-4-4400000000000000−2i22i22i2−2i2000000000000000000−22222i−2i−2i2i000000000000000
χ658-8-8-8-8888000000000000000000000000000000000000000000000000000000000

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