Finite Group Databasebeta

← Group #293413

Character table — Group #293413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111222244444488888888888161616161616161616161616161616161616161616161616
order12222222222244444444444444444244444444444444488888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11-1-1-1111-1-1-111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111-1-1-1-11-1-1-1-1-11-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111-1-11-1-11111-1-1-1-111-11-11111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-11-1-11111-1-1-1-1-1-1-11-11-1-1-1-1-1-111111111
χ711111111111111111111-1-11-1-1-1-1-1-1-111111-1-11-111-1-1-1-11111-1-1-1-1
χ811111111111111111111-1-11-1-1-1-1-1-1-1111-1-1-1-11-1-1-11111-1-1-1-11111
χ9111111111111-1-11111-1-111-11111-1-1-1-11-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-11111-1-111-11111-1-1-1-11-1-1-1-1-11111-1-111-1-111-1-111
χ11111111111111-1-11111-1-111-111-1-111-11-1111-11-1-1-1-1-1-111-1-11111-1-1
χ12111111111111-1-11111-1-111-111-1-111-11-11-1-1-11-1-11111-1-111-1-1-1-111
χ13111111111111-1-11111-1-1-1-1-1-1-111-1-111-11111-1-11-1-111-1-1-1-111-1-111
χ14111111111111-1-11111-1-1-1-1-1-1-111-1-111-11-1-11-1-1111-1-11111-1-111-1-1
χ15111111111111-1-11111-1-1-1-1-1-1-1-1-1111-11-111111-1-1-1-1-11111-1-1-1-111
χ16111111111111-1-11111-1-1-1-1-1-1-1-1-1111-11-1-1-1111-11111-1-1-1-11111-1-1
χ1722222222222222-2-2-2-2-2-20020022220000000-20-200000000000000
χ1822222222222222-2-2-2-2-2-200200-2-2-2-2000000020200000000000000
χ19222222222222-2-2-2-2-2-22200-20022-2-2000000020-200000000000000
χ20222222222222-2-2-2-2-2-22200-200-2-2220000000-20200000000000000
χ2122222222-2-2-2-2222-2-222-222-2-2-20000-200000200000000000000000
χ2222222222-2-2-2-2222-2-222-2-2-2-2220000200000-200000000000000000
χ2322222222-2-2-2-222-222-2-2200-200000002-2-200002000000000000000
χ2422222222-2-2-2-222-222-2-2200-20000000-2220000-2000000000000000
χ2522222222-2-2-2-2-2-22-2-22-22222-2-20000200000-200000000000000000
χ2622222222-2-2-2-2-2-22-2-22-22-2-22220000-200000200000000000000000
χ2722222222-2-2-2-2-2-2-222-22-2002000000022-20000-2000000000000000
χ2822222222-2-2-2-2-2-2-222-22-20020000000-2-2200002000000000000000
χ292-22-2-22-222-22-20022-2-2002i−2i02i−2i0000000000000000002-2002i−2i0000
χ302-22-2-22-222-22-20022-2-2002i−2i02i−2i000000000000000000-2200−2i2i0000
χ312-22-2-22-222-22-20022-2-200−2i2i0−2i2i0000000000000000002-200−2i2i0000
χ322-22-2-22-222-22-20022-2-200−2i2i0−2i2i000000000000000000-22002i−2i0000
χ332-22-2-22-22-22-22002-22-2002i−2i0−2i2i00000000000000002-2002i−2i000000
χ342-22-2-22-22-22-22002-22-2002i−2i0−2i2i0000000000000000-2200−2i2i000000
χ352-22-2-22-22-22-22002-22-200−2i2i02i−2i00000000000000002-200−2i2i000000
χ362-22-2-22-22-22-22002-22-200−2i2i02i−2i0000000000000000-22002i−2i000000
χ3744-44-44-4-444-4-400000000000004-400000000000000000000000000
χ3844-44-44-4-444-4-40000000000000-4400000000000000000000000000
χ3944-44-44-4-4-4-4440000000000000004i−4i000000000000000000000000
χ4044-44-44-4-4-4-444000000000000000−4i4i000000000000000000000000
χ4144-4-44-4-4400004i−4i00000000000000000002i−2i00002-2000000000000
χ4244-4-44-4-4400004i−4i0000000000000000000−2i2i0000-22000000000000
χ4344-4-44-4-440000−4i4i00000000000000000002i−2i0000-22000000000000
χ4444-4-44-4-440000−4i4i0000000000000000000−2i2i00002-2000000000000
χ454-44-4-44-444-44-400-4-44400000000000000000000000000000000000
χ464-44-4-44-44-44-4400-44-4400000000000000000000000000000000000
χ474-4-4-4444-44-4-440000000000000000000000000000000000000002i2−2i2
χ484-4-4-4444-44-4-44000000000000000000000000000000000000000−2i22i2
χ494-4-4-4444-4-444-400000000000000000000000000000000000002i2−2i200
χ504-4-4-4444-4-444-40000000000000000000000000000000000000−2i22i200
χ51888-8-8-88-8000000000000000000000000000000000000000000000
χ528-8888-8-8-8000000000000000000000000000000000000000000000
χ538-8-88-8-888000000000000000000000000000000000000000000000

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