Finite Group Databasebeta

← Group #342009

Character table — Group #342009

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444222444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11-1-11-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-111-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1111-1-1-1-1-1-111-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-111-1-111-1-1-1-1-1-111-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-111111111-1-1-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-11111-1-1111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-111111-1-1-1-111-1-1-1-1-11
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-111-1-11111111-1
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1-1-11-1
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-111-1-111-1-11111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11111111-1-1-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-111-1-111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-1-1-1-1-111-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-11111-1-11111-1-1-1-1
χ17222222222-22-2-222-2-2-2000000002222-2-2-2-200000000000022-2-20-22000000000000000
χ18222222222-22-2-222-2-2-2000000002222-2-2-2-2000000000000-2-22202-2000000000000000
χ19222222222-22-2-222-2-2-200000000-2-2-2-2222200000000000022220-2-2000000000000000
χ20222222222-22-2-222-2-2-200000000-2-2-2-22222000000000000-2-2-2-2022000000000000000
χ2122222222-22-222-2-22-2-22222-2-2-2-2000000000000000022220000-200-200000000000000
χ2222222222-22-222-2-22-2-22222-2-2-2-20000000000000000-2-2-2-20000200200000000000000
χ2322222222-22-222-2-22-2-2-2-2-2-22222000000000000000022-2-20000200-200000000000000
χ2422222222-22-222-2-22-2-2-2-2-2-222220000000000000000-2-2220000-200200000000000000
χ25222-2-22-2-20-202-20020022-2-2000022−2−222−2−22222−2−2−2−22i−2i2i−2i000000000000i2−i2i2−i2000000
χ26222-2-22-2-20-202-20020022-2-2000022−2−222−2−22222−2−2−2−2−2i2i−2i2i000000000000−i2i2−i2i2000000
χ27222-2-22-2-20-202-20020022-2-20000−2−222−2−222−2−2−2−222222i−2i2i−2i000000000000−i2i2−i2i2000000
χ28222-2-22-2-20-202-20020022-2-20000−2−222−2−222−2−2−2−22222−2i2i−2i2i000000000000i2−i2i2−i2000000
χ29222-2-22-2-20-202-200200-2-222000022−2−222−2−2−2−2−2−222222i−2i−2i2i000000000000−i2i2i2−i2000000
χ30222-2-22-2-20-202-200200-2-222000022−2−222−2−2−2−2−2−22222−2i2i2i−2i000000000000i2−i2−i2i2000000
χ31222-2-22-2-20-202-200200-2-2220000−2−222−2−2222222−2−2−2−22i−2i−2i2i000000000000i2−i2−i2i2000000
χ32222-2-22-2-20-202-200200-2-2220000−2−222−2−2222222−2−2−2−2−2i2i2i−2i000000000000−i2i2i2−i2000000
χ332-2222-2-2-2-20-200220002−22−222−2−200002-22-222−2−222−2−200002i−2i2i−2i000000000000i2−i2i2−i200
χ342-2222-2-2-2-20-200220002−22−222−2−200002-22-222−2−222−2−20000−2i2i−2i2i000000000000−i2i2−i2i200
χ352-2222-2-2-2-20-200220002−22−222−2−20000-22-22−2−222−2−22200002i−2i−2i2i000000000000i2−i2−i2i200
χ362-2222-2-2-2-20-200220002−22−222−2−20000-22-22−2−222−2−2220000−2i2i2i−2i000000000000−i2i2i2−i200
χ372-2222-2-2-2-20-20022000−22−22−2−22200002-22-2−2−222−2−22200002i−2i2i−2i000000000000−i2i2−i2i200
χ382-2222-2-2-2-20-20022000−22−22−2−22200002-22-2−2−222−2−2220000−2i2i−2i2i000000000000i2−i2i2−i200
χ392-2222-2-2-2-20-20022000−22−22−2−2220000-22-2222−2−222−2−200002i−2i−2i2i000000000000−i2i2i2−i200
χ402-2222-2-2-2-20-20022000−22−22−2−2220000-22-2222−2−222−2−20000−2i2i2i−2i000000000000i2−i2−i2i200
χ412-2-2-222-222-2-2222-2-22-200000000000000002i−2i2i−2i2i−2i2i−2i0000000000002i−2i2-20000000000
χ422-2-2-222-222-2-2222-2-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000000−2i2i-220000000000
χ432-2-2-222-222-2-2222-2-22-20000000000000000−2i2i−2i2i−2i2i−2i2i0000000000002i−2i-220000000000
χ442-2-2-222-222-2-2222-2-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000000−2i2i2-20000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-4040-4400-400000000002222−22−22−22−2222220000000000000000000000000000000000
χ47444-4-44-4-4040-4400-40000000000−22−2222222222−22−220000000000000000000000000000000000
χ4844-44-4-4-440000000000000022−2222−222i2−2i22i2−2i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ4944-44-4-4-440000000000000022−2222−22−2i22i2−2i22i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5044-44-4-4-4400000000000000−2222−22222i2−2i22i2−2i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5144-44-4-4-4400000000000000−2222−2222−2i22i2−2i22i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5244-4-44-44-440-400-44000000000004i−4i−4i4i00000000000000000000000000000000000000
χ5344-4-44-44-440-400-4400000000000−4i4i4i−4i00000000000000000000000000000000000000
χ5444-4-44-44-4-404004-400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ5544-4-44-44-4-404004-40000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ564-4444-4-4-440400-4-400022−2222−22−22−222222000000000000000000000000000000000000000000
χ574-4444-4-4-440400-4-4000−2222−22222222−22−22000000000000000000000000000000000000000000
χ584-44-4-4-444000000000022−22−22220000000022−22−222222-2-2-2-22200000000000000000000000000
χ594-44-4-4-444000000000022−22−222200000000−222222−22-2-22222-2-200000000000000000000000000
χ604-44-4-4-4440000000000−222222−220000000022−22−2222-2-22222-2-200000000000000000000000000
χ614-44-4-4-4440000000000−222222−2200000000−222222−2222-2-2-2-22200000000000000000000000000
χ624-4-44-444-40404-400-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ634-4-44-444-40404-400-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ644-4-44-444-40-40-440040000004-4-44000000000000000000000000000000000000000000
χ654-4-44-444-40-40-44004000000-444-4000000000000000000000000000000000000000000
χ664-4-4-444-4444-4-4-44-44-4400000000000000000000000000000000000000000000000000
χ674-4-4-444-44-444-4-4-4444-400000000000000000000000000000000000000000000000000
χ684-4-4-444-44-4-4444-44-4-4400000000000000000000000000000000000000000000000000

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