Finite Group Databasebeta

← Group #104751

Character table — Group #104751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222222224444448888888888161616161616161616161616161616161616161616161616
order12222222222244444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1
χ9222222222222222222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ10222222222222222222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ11222222222222-2-2-2-2-2-222-2-22-2000000000000002200-2-2000000000000
χ12222222222222-2-2-2-2-2-222-2-22-200000000000000-2-20022000000000000
χ13222222222222-2-2-2-2-2-2-2-222-220000000000002200-2-200000000000000
χ14222222222222-2-2-2-2-2-2-2-222-22000000000000-2-2002200000000000000
χ1522222222-2-2-2-22222-2-222-2-2-220000000000000000000000002i2i−2i−2i0000
χ1622222222-2-2-2-22222-2-222-2-2-22000000000000000000000000−2i−2i2i2i0000
χ1722222222-2-2-2-22222-2-2-2-2222-200000000000000000000000000002i2i−2i−2i
χ1822222222-2-2-2-22222-2-2-2-2222-20000000000000000000000000000−2i−2i2i2i
χ1922222222-2-2-2-2-2-2-2-2222222-2-2000000000000000000002i2i−2i−2i00000000
χ2022222222-2-2-2-2-2-2-2-2222222-2-200000000000000000000−2i−2i2i2i00000000
χ2122222222-2-2-2-2-2-2-2-222-2-2-2-2220000000022-2-200000000000000000000
χ2222222222-2-2-2-2-2-2-2-222-2-2-2-22200000000-2-22200000000000000000000
χ232-2-22-2-2222-22-222-2-22-200000000002i2i−2i−2i00000000000000002−22−2i2−i2i2−i2
χ242-2-22-2-2222-22-222-2-22-200000000002i2i−2i−2i0000000000000000−22−22−i2i2−i2i2
χ252-2-22-2-2222-22-222-2-22-20000000000−2i−2i2i2i00000000000000002−22−2−i2i2−i2i2
χ262-2-22-2-2222-22-222-2-22-20000000000−2i−2i2i2i0000000000000000−22−22i2−i2i2−i2
χ272-2-22-2-222-22-2222-2-2-220000002i2i−2i−2i00000000000000000000i2−i2−i2i22−2−22
χ282-2-22-2-222-22-2222-2-2-220000002i2i−2i−2i00000000000000000000−i2i2i2−i2−222−2
χ292-2-22-2-222-22-2222-2-2-22000000−2i−2i2i2i00000000000000000000i2−i2−i2i2−222−2
χ302-2-22-2-222-22-2222-2-2-22000000−2i−2i2i2i00000000000000000000−i2i2i2−i22−2−22
χ314444-4-4-4-444-4-4000000000000000000000000000000002-22-200000000
χ324444-4-4-4-444-4-400000000000000000000000000000000-22-2200000000
χ334444-4-4-4-4-4-444000000000000000000000000000000002i−2i−2i2i00000000
χ344444-4-4-4-4-4-44400000000000000000000000000000000−2i2i2i−2i00000000
χ3544-4-44-44-40000000000004i−4i002-22-22i−2i2i−2i000000000000000000000000
χ3644-4-44-44-40000000000004i−4i00-22-22−2i2i−2i2i000000000000000000000000
χ3744-4-44-44-4000000000000−4i4i002-22-2−2i2i−2i2i000000000000000000000000
χ3844-4-44-44-4000000000000−4i4i00-22-222i−2i2i−2i000000000000000000000000
χ3944-4-4-44-4400004i−4i4i−4i00000000000000000000002-2002i−2i000000000000
χ4044-4-4-44-4400004i−4i4i−4i0000000000000000000000-2200−2i2i000000000000
χ4144-4-4-44-440000−4i4i−4i4i00000000000000000000002-200−2i2i000000000000
χ4244-4-4-44-440000−4i4i−4i4i0000000000000000000000-22002i−2i000000000000
χ434-44-44-4-4400004i−4i−4i4i000000000000000000002i−2i002-200000000000000
χ444-44-44-4-4400004i−4i−4i4i00000000000000000000−2i2i00-2200000000000000
χ454-44-44-4-440000−4i4i4i−4i000000000000000000002i−2i00-2200000000000000
χ464-44-44-4-440000−4i4i4i−4i00000000000000000000−2i2i002-200000000000000
χ474-44-4-444-400000000004i−4i00002i−2i−2i2i2-2-22000000000000000000000000
χ484-44-4-444-400000000004i−4i0000−2i2i2i−2i-222-2000000000000000000000000
χ494-44-4-444-40000000000−4i4i00002i−2i−2i2i-222-2000000000000000000000000
χ504-44-4-444-40000000000−4i4i0000−2i2i2i−2i2-2-22000000000000000000000000
χ514-4-4444-4-44-4-44000000000000000000002i−2i2i−2i00000000000000000000
χ524-4-4444-4-44-4-4400000000000000000000−2i2i−2i2i00000000000000000000
χ534-4-4444-4-4-444-4000000000000000000002i−2i−2i2i00000000000000000000
χ544-4-4444-4-4-444-400000000000000000000−2i2i2i−2i00000000000000000000
χ554-4-44-4-4444-44-4-4-444-4400000000000000000000000000000000000000
χ564-4-44-4-444-44-44-4-4444-400000000000000000000000000000000000000

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