Finite Group Databasebeta

← Group #331849

Character table — Group #331849

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111111112222222244888888888888888816161616161616161616161616161616323232
order12222222444444444422228888888888882224444488888888444
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-111-1-1-1-1-1-11111-111-111-1-1-1-1-1-1-11-1
χ31111111111111111111111-1-111-1-111-1-1-1-111-1111-11-1-111-1-1-1-1-1-11
χ41111111111111111111111-1-1-1-1-1-1-1-1111111-11-11-1-1-1-1-1-111111-1-1
χ511111111111111111111-1-1111111111111-1-11-1-111-1-1-11111-1-1-1-1-1
χ611111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1111-11
χ711111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1-11111-1-11111-1
χ811111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1111-1-111-1-1-111
χ9111111111111111111-1-111111111111111-1-1-111-1-1111-1-1-1-111-1-1-1
χ10111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-11-11
χ11111111111111111111-1-111-1-111-1-111-1-1-1-1-1-1111-111-1-1-1-111-1-111-1
χ12111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-11-1-1-111-1-111-111
χ13111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ14111111111111111111-1-1-1-111-1-111-1-1-1-1-1-111-1-11-1-11-1-1111111-11-1
χ15111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1111-1-1-11-111-1-11111-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-11-1111111-1-1-1-11-1-1
χ17222222222-22-22-22-2-2-222002200-2-200000000200-2-2000000000000
χ18222222222-22-22-22-2-2-22200-2-2002200000000-200-22000000000000
χ19222222222-22-22-22-2-2-2-2-2002200-2-200000000-20022000000000000
χ20222222222-22-22-22-2-2-2-2-200-2-20022000000002002-2000000000000
χ2122222222-22-22-22-22-2-20022002200-2-20000000-2-200200000000000
χ2222222222-22-22-22-22-2-2002200-2-200220000000-2200-200000000000
χ2322222222-22-22-22-22-2-200-2-2002200-2-200000002200-200000000000
χ2422222222-22-22-22-22-2-200-2-200-2-2002200000002-200200000000000
χ252-2-222-22-222-2-222-2-22-200000000000000002-200000000002i−2i2i−2i000
χ262-2-222-22-222-2-222-2-22-200000000000000002-20000000000−2i2i−2i2i000
χ272-2-222-22-222-2-222-2-22-20000000000000000-2200000000002i−2i−2i2i000
χ282-2-222-22-222-2-222-2-22-20000000000000000-220000000000−2i2i2i−2i000
χ2944444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000
χ304444-4-4-4-44040-40-40004-4000000000000000000000000000000000
χ314444-4-4-4-44040-40-4000-44000000000000000000000000000000000
χ324444-4-4-4-4-40-40404000000000000000000000000000002i2−2i20000000
χ334444-4-4-4-4-40-4040400000000000000000000000000000−2i22i20000000
χ3444-4-444-4-400000000000000002i2−2i22i2−2i20022-2-20000000000000000000
χ3544-4-444-4-400000000000000002i2−2i2−2i22i200-2-2220000000000000000000
χ3644-4-444-4-40000000000000000−2i22i22i2−2i200-2-2220000000000000000000
χ3744-4-444-4-40000000000000000−2i22i2−2i22i20022-2-20000000000000000000
χ3844-4-4-4-444040-40-4040000000000000000000000000022−22000000000
χ3944-4-4-4-444040-40-40400000000000000000000000000−2222000000000
χ4044-4-4-4-4440-404040-400004-40000000000000000000000000000000
χ4144-4-4-4-4440-404040-40000-440000000000000000000000000000000
χ424-44-4-444-404040-40-40000000000004i−4i00000000000000000000000
χ434-44-4-444-404040-40-4000000000000−4i4i00000000000000000000000
χ444-44-4-444-40-40-404040000000000000022−2222−220000000000000000000
χ454-44-4-444-40-40-4040400000000000000−2222−22220000000000000000000
χ464-4-444-44-44-4-444-4-44-4400000000000000000000000000000000000
χ474-4-444-44-4-444-4-444-4-4400000000000000000000000000000000000
χ484-4-444-44-4-4-444-4-4444-400000000000000000000000000000000000
χ494-4-44-44-4440-40-40400000000000000022−22−22220000000000000000000
χ504-4-44-44-4440-40-404000000000000000−222222−220000000000000000000
χ514-4-44-44-44-404040-400000004-400000000000000000000000000000
χ524-4-44-44-44-404040-40000000-4400000000000000000000000000000
χ538-88-88-8-88000000000000000000000000000000000000000000000

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