Finite Group Databasebeta

← Group #245488

Character table — Group #245488

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222222444888888888888888816161616161616161616161616161616161616161616
order12222244444444422444444888888882244444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-1-1-111-11111-1-1-1111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-111-1-1-1-11-11-1-1-11111-1-1-1111-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-11-11-11-111111111-11-11-1-1-1-1-1-11-1-1111-1-111-1-1
χ61111111111111111-11-11-11-111-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-111-1-111
χ71111111111111111-11-11-11-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-11111111-1-111
χ81111111111111111-11-11-11-1-1-1-1-11111-1-11-111-1111-111-1-1-1-1-111-1-1
χ9111111111111111-11-11-11-1111111111-1-11-1-1-1-11-1-11111-1-1-1-1-1-111
χ10111111111111111-11-11-11-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1111111-1-1
χ11111111111111111-11-11-11-11-1-111-1-1-1-1-111111-11-1-1-1-1-11-1-11111-1-1
χ12111111111111111-11-11-11-11-1-1-1-11111-11-1111-1-111-1-1-1-111-1-1-1-111
χ13111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1111-1111-1-11-1-111-1-1-1-1
χ14111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11-11111-1-11-1-1-111-1-11111
χ15111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11-1-11-111-1111-1-1-1-11111
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-111-11111-1-1-1-1
χ17222222-22222-2-2-2-222-2-222-2-200000000-2000002000000000000000
χ18222222-22222-2-2-2-22-2-222-2-2200000000200000-2000000000000000
χ19222222-22222-2-2-2-2-222-2-222-200000000200000-2000000000000000
χ20222222-22222-2-2-2-2-2-222-2-22200000000-2000002000000000000000
χ212222-2-2222-2-222-2-2020-20-2020022000000-20000200000-200000000
χ222222-2-2222-2-222-2-2020-20-20200-2-200000020000-200000200000000
χ232222-2-2222-2-222-2-20-202020-2002200000020000-200000-200000000
χ242222-2-2222-2-222-2-20-202020-200-2-2000000-20000200000200000000
χ252222-2-22-2-2222-22-220-20-2020220000000-202000000-200000000000
χ262222-2-22-2-2222-22-220-20-2020-2-2000000020-2000000200000000000
χ272222-2-22-2-2222-22-2-202020-2022000000020-2000000-200000000000
χ282222-2-22-2-2222-22-2-202020-20-2-20000000-202000000200000000000
χ292222-2-2-222-2-2-2-22202020-20-200000000000000002-200002-2000000
χ302222-2-2-222-2-2-2-22202020-20-20000000000000000-220000-22000000
χ312222-2-2-222-2-2-2-2220-20-2020200000000000000002-20000-22000000
χ322222-2-2-222-2-2-2-2220-20-202020000000000000000-2200002-2000000
χ332222-2-2-2-2-222-22-222020-20-200000000000002-2000002-2000000000
χ342222-2-2-2-2-222-22-222020-20-20000000000000-2200000-22000000000
χ352222-2-2-2-2-222-22-22-20-2020200000000000002-200000-22000000000
χ362222-2-2-2-2-222-22-22-20-202020000000000000-22000002-2000000000
χ374444444-4-4-4-44-4-4400000000000000000000000000000000000000
χ38444444-4-4-4-4-4-444-400000000000000000000000000000000000000
χ394-44-44-404-44-400000000000000000000000000000000000000002i2−2i2
χ404-44-44-404-44-40000000000000000000000000000000000000000−2i22i2
χ414-44-44-40-44-44000000000000000000000000000000000000002i2−2i200
χ424-44-44-40-44-4400000000000000000000000000000000000000−2i22i200
χ434-44-4-4404-4-4400000000000000002i22i2−2i2−2i20000000000000000000000
χ444-44-4-4404-4-440000000000000000−2i2−2i22i22i20000000000000000000000
χ454-44-4-440-444-40000000000000000000000000000000000002i2−2i20000
χ464-44-4-440-444-4000000000000000000000000000000000000−2i22i20000
χ474-4-440040000-4000000000002i2−2i222−222i−2i2i−2i0000000000000000000000
χ484-4-440040000-4000000000002i2−2i2−2222−2i2i−2i2i0000000000000000000000
χ494-4-440040000-400000000000−2i22i222−22−2i2i−2i2i0000000000000000000000
χ504-4-440040000-400000000000−2i22i2−22222i−2i2i−2i0000000000000000000000
χ5188-8-80000000000000000000000022−22−22220000000000000000000000
χ5288-8-800000000000000000000000−222222−220000000000000000000000
χ538-8-8800-80000800000000000000000000000000000000000000000

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