Finite Group Databasebeta

← Group #333320

Character table — Group #333320

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444244444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-11-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111111-11-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111111-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1111-1-111-1-1-1-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-11111-1-11111-11
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1111111-1-11-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111-11-1-111111-1-1-1-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-11111-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-111-1-11111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11-1-11-1-1-1-11111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-111111-1-1-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-11111-1111111-1-1-1-1-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111
χ17222222222-22-22-22-2-2-2000022220000-2-2-2-20000000000002222-20-2000000000000000
χ18222222222-22-22-22-2-2-2000022220000-2-2-2-2000000000000-2-2-2-2202000000000000000
χ19222222222-22-22-22-2-2-20000-2-2-2-20000222200000000000022-2-220-2000000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-200002222000000000000-2-222-202000000000000000
χ2122222222-22-22-22-22-2-222220000-2-2-2-200000000000022-2-2000002000-2000000000000
χ2222222222-22-22-22-22-2-222220000-2-2-2-2000000000000-2-22200000-20002000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-200002222000000000000222200000-2000-2000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200002222000000000000-2-2-2-20000020002000000000000
χ25222-2-2-22-220-20-202000i2i2−i2−i22i2i−2i−2ii2i2−i2−i200002222−2−2−2−200002-22i−2i00000000002−200i2−i200
χ26222-2-2-22-220-20-202000i2i2−i2−i22i2i−2i−2ii2i2−i2−i200002222−2−2−2−20000-22−2i2i0000000000−2200−i2i200
χ27222-2-2-22-220-20-202000i2i2−i2−i2−2i−2i2i2ii2i2−i2−i20000−2−2−2−2222200002-2−2i2i0000000000−2200i2−i200
χ28222-2-2-22-220-20-202000i2i2−i2−i2−2i−2i2i2ii2i2−i2−i20000−2−2−2−222220000-222i−2i00000000002−200−i2i200
χ29222-2-2-22-220-20-202000−i2−i2i2i22i2i−2i−2i−i2−i2i2i20000−2−2−2−2222200002-22i−2i0000000000−2200−i2i200
χ30222-2-2-22-220-20-202000−i2−i2i2i22i2i−2i−2i−i2−i2i2i20000−2−2−2−222220000-22−2i2i00000000002−200i2−i200
χ31222-2-2-22-220-20-202000−i2−i2i2i2−2i−2i2i2i−i2−i2i2i200002222−2−2−2−200002-2−2i2i00000000002−200−i2i200
χ32222-2-2-22-220-20-202000−i2−i2i2i2−2i−2i2i2i−i2−i2i2i200002222−2−2−2−20000-222i−2i0000000000−2200i2−i200
χ332-22-22-2-2202020-20-20000002−22−22i−2i2i−2i22−2−2i2i2−i2−i2i2i2−i2−i22-22i−2i0000000000002−200i2−i20000
χ342-22-22-2-2202020-20-20000002−22−22i−2i2i−2i22−2−2i2i2−i2−i2i2i2−i2−i2-22−2i2i000000000000−2200−i2i20000
χ352-22-22-2-2202020-20-20000002−22−2−2i2i−2i2i22−2−2−i2−i2i2i2−i2−i2i2i22-2−2i2i0000000000002−200−i2i20000
χ362-22-22-2-2202020-20-20000002−22−2−2i2i−2i2i22−2−2−i2−i2i2i2−i2−i2i2i2-222i−2i000000000000−2200i2−i20000
χ372-22-22-2-2202020-20-2000000−22−222i−2i2i−2i−2−222−i2−i2i2i2−i2−i2i2i22-22i−2i000000000000−2200−i2i20000
χ382-22-22-2-2202020-20-2000000−22−222i−2i2i−2i−2−222−i2−i2i2i2−i2−i2i2i2-22−2i2i0000000000002−200i2−i20000
χ392-22-22-2-2202020-20-2000000−22−22−2i2i−2i2i−2−222i2i2−i2−i2i2i2−i2−i22-2−2i2i000000000000−2200i2−i20000
χ402-22-22-2-2202020-20-2000000−22−22−2i2i−2i2i−2−222i2i2−i2−i2i2i2−i2−i2-222i−2i0000000000002−200−i2i20000
χ412-2-2-2-2222-2-222-2-222-2200000000000000002-22-22-22-2000000000002-202-20000000000
χ422-2-2-2-2222-2-222-2-222-2200000000000000002-22-22-22-200000000000-220-220000000000
χ432-2-2-2-2222-2-222-2-222-220000000000000000-22-22-22-22000000000002-20-220000000000
χ442-2-2-2-2222-2-222-2-222-220000000000000000-22-22-22-2200000000000-2202-20000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-44-4-404040-40002i22i2−2i2−2i20000−2i2−2i22i22i200000000000000000000000000000000000000
χ47444-4-4-44-4-404040-4000−2i2−2i22i22i200002i22i2−2i2−2i200000000000000000000000000000000000000
χ4844-44-4-4-44040-40-404004i−4i4i−4i0000000000000000000000000000000000000000000000
χ4944-44-4-4-44040-40-40400−4i4i−4i4i0000000000000000000000000000000000000000000000
χ5044-44-4-4-440-404040-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ5144-44-4-4-440-404040-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ5244-4-444-4-4000000000022−22−2222000000002i2−2i22i2−2i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5344-4-444-4-4000000000022−22−222200000000−2i22i2−2i22i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5444-4-444-4-40000000000−222222−22000000002i2−2i22i2−2i2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5544-4-444-4-40000000000−222222−2200000000−2i22i2−2i22i22i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ564-444-44-4-4000000000000002i2−2i2−2i22i222−22−22220000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ574-444-44-4-4000000000000002i2−2i2−2i22i2−222222−2200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ584-444-44-4-400000000000000−2i22i22i2−2i222−22−222200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ594-444-44-4-400000000000000−2i22i22i2−2i2−222222−220000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ604-44-44-4-440-40-4040400000022−2222−220000−22−2222220000000000000000000000000000000000
χ614-44-44-4-440-40-40404000000−2222−222200002222−22−220000000000000000000000000000000000
χ624-4-444-44-44040-40-40000000000000004i−4i−4i4i0000000000000000000000000000000000
χ634-4-444-44-44040-40-4000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ644-4-444-44-4-40-40404000000000000000000022−2222−22−2222−222200000000000000000000000000
χ654-4-444-44-4-40-404040000000000000000000−2222−222222−2222−2200000000000000000000000000
χ664-4-4-4-444444-4-444-4-4-4400000000000000000000000000000000000000000000000000
χ674-4-4-4-44444-4-444-4-444-400000000000000000000000000000000000000000000000000
χ684-4-4-4-4444-444-4-444-44-400000000000000000000000000000000000000000000000000

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