Finite Group Databasebeta

← Group #306721

Character table — Group #306721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888244444448888882
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111111111-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ51111111111111111111111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-1-111-1-1111-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111-1-11
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-11-1-1111-1-111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-111-111-1-11111-1
χ911111111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-111-1-11
χ1011111111111111111-1-1-1-11111111-1-11111-1-11111-1-1-1-11111111-1-1-1-1-1-1-111-1-111-1
χ1111111111111111111-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-11111-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-11111111-1-1-1-1-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-1-111111
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111111-1-11-1-1-1-1-1-1111
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-1111111-1-1-1
χ17222222222-22-22-22-2-20000-222222200-2-22200-2-2000000000000-200000000000000
χ18222222222-22-22-22-2-20000-22222-2-20022-2-200-2-2000000000000200000000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-22200-2-2-2-20022000000000000200000000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-20022220022000000000000-200000000000000
χ2122222222-22-22-22-22-22222-2000000220000-2-200-2-2000022000000000-2000000000
χ2222222222-22-22-22-22-22222-2000000-2-20000-2-200220000-2-20000000002000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000002200002200220000-2-2000000000-2000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000-2-200002200-2-20000220000000002000000000
χ25222-22-2-2-22-2-222-2-22-22i2i−2i−2i20000000000002i−2i000000000000000000002i−2i00002-20
χ26222-22-2-2-22-2-222-2-22-22i2i−2i−2i20000000000002i−2i00000000000000000000−2i2i0000-220
χ27222-22-2-2-22-2-222-2-22-2−2i−2i2i2i2000000000000−2i2i000000000000000000002i−2i0000-220
χ28222-22-2-2-22-2-222-2-22-2−2i−2i2i2i2000000000000−2i2i00000000000000000000−2i2i00002-20
χ29222-22-2-2-2-222-2-222-2-20000200002-2002-2000000002i2i−2i−2i0000000002i−2i0000000000
χ30222-22-2-2-2-222-2-222-2-20000200002-2002-200000000−2i−2i2i2i000000000−2i2i0000000000
χ31222-22-2-2-2-222-2-222-2-2000020000-2200-22000000002i2i−2i−2i000000000−2i2i0000000000
χ32222-22-2-2-2-222-2-222-2-2000020000-2200-2200000000−2i−2i2i2i0000000002i−2i0000000000
χ33222-22-2-2-2-2-222-2-22222i2i−2i−2i-200002-200-2200−2i2i0000000000000002i−2i000000000000
χ34222-22-2-2-2-2-222-2-22222i2i−2i−2i-20000-22002-200−2i2i000000000000000−2i2i000000000000
χ35222-22-2-2-2-2-222-2-2222−2i−2i2i2i-200002-200-22002i−2i000000000000000−2i2i000000000000
χ36222-22-2-2-2-2-222-2-2222−2i−2i2i2i-20000-22002-2002i−2i0000000000000002i−2i000000000000
χ372-2-2222-2-202020-20-202i−2i2i−2i022−2−2002-20000002−200i2−i2i2−i22i−2ii2i2−i2−i200000000002−2000
χ382-2-2222-2-202020-20-202i−2i2i−2i022−2−200-220000002−200i2−i2i2−i2−2i2i−i2−i2i2i20000000000−22000
χ392-2-2222-2-202020-20-202i−2i2i−2i0−2−222002-2000000−2200−i2i2−i2i22i−2i−i2−i2i2i20000000000−22000
χ402-2-2222-2-202020-20-202i−2i2i−2i0−2−22200-22000000−2200−i2i2−i2i2−2i2ii2i2−i2−i200000000002−2000
χ412-2-2222-2-202020-20-20−2i2i−2i2i022−2−2002-20000002−200−i2i2−i2i2−2i2i−i2−i2i2i200000000002−2000
χ422-2-2222-2-202020-20-20−2i2i−2i2i022−2−200-220000002−200−i2i2−i2i22i−2ii2i2−i2−i20000000000−22000
χ432-2-2222-2-202020-20-20−2i2i−2i2i0−2−222002-2000000−2200i2−i2i2−i2−2i2ii2i2−i2−i20000000000−22000
χ442-2-2222-2-202020-20-20−2i2i−2i2i0−2−22200-22000000−2200i2−i2i2−i22i−2i−i2−i2i2i200000000002−2000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-44-4-4-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ4744-44-4-44-4000000000000002i2−2i22i2−2i20000000000002i2−2i20000002-22-2000000000000000
χ4844-44-4-44-4000000000000002i2−2i22i2−2i2000000000000−2i22i2000000-22-22000000000000000
χ4944-44-4-44-400000000000000−2i22i2−2i22i20000000000002i2−2i2000000-22-22000000000000000
χ5044-44-4-44-400000000000000−2i22i2−2i22i2000000000000−2i22i20000002-22-2000000000000000
χ514-444-4-4-4440-40-40400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ524-444-4-4-4440-40-4040000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ534-444-4-4-44-404040-400000004i−4i−4i4i000000000000000000000000000000000000000
χ544-444-4-4-44-404040-40000000−4i4i4i−4i000000000000000000000000000000000000000
χ554-44-4-444-44040-40-4000000000000000004i−4i0000000000000000000000000000000
χ564-44-4-444-44040-40-400000000000000000−4i4i0000000000000000000000000000000
χ574-44-4-444-4-40-40404000000000000000000000000000000000000000000022−2200000
χ584-44-4-444-4-40-404040000000000000000000000000000000000000000000−222200000
χ594-4-4444-4-40-40-404040000002222−22−220000000000−2222000000000000000000000000000
χ604-4-4444-4-40-40-40404000000−22−222222000000000022−22000000000000000000000000000
χ614-4-4-44-444040-40-40400000000000000000000000022−22−2222000000000000000000000
χ624-4-4-44-444040-40-404000000000000000000000000−222222−22000000000000000000000
χ634-4-4-44-4440-404040-404-4-4400000000000000000000000000000000000000000000
χ644-4-4-44-4440-404040-40-444-400000000000000000000000000000000000000000000
χ6588-8-8-88-88000000000000000000000000000000000000000000000000000000000

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