Finite Group Databasebeta

← Group #223191

Character table — Group #223191

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222222224444444444444444444444444488888888888888888888888888816161616161616161616
order12222222444444444444222244444444444444888888884444444888888888888888888884444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ611111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111
χ811111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1iiii−i−i−i−i-1-1111-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−i11-1-11-1i−ii−i
χ10111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1iiii−i−i−i−i-1-11-1-111ii−i−i−i−iii−i−iiiiiii−i−i−i−i-1-111-11−ii−ii
χ11111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1−i−i−i−iiiii-1-1111-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii11-1-11-1−ii−ii
χ12111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1−i−i−i−iiiii-1-11-1-111−i−iiiii−i−iii−i−i−i−i−i−iiiii-1-111-11i−ii−i
χ13111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i11111-1-1ii−i−iii−i−iii−i−i−i−i−i−iiiii-1-1111-1−ii−ii
χ14111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i111-1-111ii−i−i−i−iii−i−iii−i−i−i−iiiii11-1-1-11i−ii−i
χ15111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii11111-1-1−i−iii−i−iii−i−iiiiiii−i−i−i−i-1-1111-1i−ii−i
χ16111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii111-1-111−i−iiiii−i−iii−i−iiiii−i−i−i−i11-1-1-11−ii−ii
χ1711111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-11-11-1-1-111-1-1
χ1811111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-11-1111-1-111
χ1911111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111111111111-1-1-1-1-1-111-1-1111-11-1-1-1-1-111
χ2011111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-11-111111-1-1
χ2111111111-1-1-1-111111111-1-11111-1-111-1-1-1-111-1-111111111-11-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11-11-1-1-1-111
χ2211111111-1-1-1-111111111-1-11111-1-111-1-1-1-111-1-111111111-11-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111-11-11111-1-1
χ2311111111-1-1-1-111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1111111111111-1-1-1-111-1-111-1-1-11-11-1-111-1-1
χ2411111111-1-1-1-111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-1111111-1-111-1-11-11-111-1-111
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1iiii−i−i−i−i-11-111-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-11-11i−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1iiii−i−i−i−i-11-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iii-111-11-1−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1−i−i−i−iiiii-11-111-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-11-11−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1−i−i−i−iiiii-11-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i-111-11-1i−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111iiii−i−i−i−i1-1-111-1-1−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-1-11−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111iiii−i−i−i−i1-1-1-1-111−i−iiiii−i−i−i−iii−i−iiiii−i−i1-1-111-1i−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111−i−i−i−iiiii1-1-111-1-1ii−i−iii−i−i−i−iiiii−i−i−i−iii-111-1-11i−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111−i−i−i−iiiii1-1-1-1-111ii−i−i−i−iiiii−i−iii−i−i−i−iii1-1-111-1−iii−i
χ332222222222222-2-222-22-222-2-2-2-2-2-2-2-222-2-222-2-20000000022-20000000000000000000000000000000000
χ342222222222222-2-222-22-2-2-222-2-2222222-2-2-2-22200000000-2-2-20000000000000000000000000000000000
χ35222222222222-222-2-22-222222-2-2-2-2-2-2-2-222222200000000-2-2-20000000000000000000000000000000000
χ36222222222222-222-2-22-22-2-2-2-2-2-22222-2-222-2-2-2-20000000022-20000000000000000000000000000000000
χ3722222222-2-2-2-22-2-222-22-22222-2-2-2-222-2-222-2-2-2-2000000002-220000000000000000000000000000000000
χ3822222222-2-2-2-22-2-222-22-2-2-2-2-2-2-222-2-2-2-222222200000000-2220000000000000000000000000000000000
χ3922222222-2-2-2-2-222-2-22-2222-2-2-2-2-2-22222-2-2-2-22200000000-2220000000000000000000000000000000000
χ4022222222-2-2-2-2-222-2-22-22-2-222-2-222-2-222-2-222-2-2000000002-220000000000000000000000000000000000
χ412-222-2-2-22000022-22-2-2-2200002-200000000000022-2-222-2-20002i−2i2i−2i000000002i−2i2i−2i000000000000000000
χ422-222-2-2-22000022-22-2-2-2200002-200000000000022-2-222-2-2000−2i2i−2i2i00000000−2i2i−2i2i000000000000000000
χ432-222-2-2-22000022-22-2-2-2200002-2000000000000-2-222-2-2220002i−2i2i−2i00000000−2i2i−2i2i000000000000000000
χ442-222-2-2-22000022-22-2-2-2200002-2000000000000-2-222-2-222000−2i2i−2i2i000000002i−2i2i−2i000000000000000000
χ452-222-2-2-220000-2-22-2222-200002-20000000000002i2i−2i−2i−2i−2i2i2i0002i−2i−2i2i00000000-222-2000000000000000000
χ462-222-2-2-220000-2-22-2222-200002-20000000000002i2i−2i−2i−2i−2i2i2i000−2i2i2i−2i000000002-2-22000000000000000000
χ472-222-2-2-220000-2-22-2222-200002-2000000000000−2i−2i2i2i2i2i−2i−2i0002i−2i−2i2i000000002-2-22000000000000000000
χ482-222-2-2-220000-2-22-2222-200002-2000000000000−2i−2i2i2i2i2i−2i−2i000−2i2i2i−2i00000000-222-2000000000000000000
χ492-22-222-2-22i2i−2i−2i200-2-2020002-2002i−2i2-22i−2i00002i−2i2−22−22−22−20000000i2−i2i2−i200000000i2−i22−2i2−i22−20000000000
χ502-22-222-2-22i2i−2i−2i200-2-2020002-2002i−2i2-22i−2i00002i−2i−22−22−22−220000000−i2i2−i2i200000000−i2i2−22−i2i2−220000000000
χ512-22-222-2-22i2i−2i−2i200-2-202000-2200−2i2i-222i−2i0000−2i2i2−22−22−22−20000000i2−i2i2−i200000000−i2i2−22−i2i2−220000000000
χ522-22-222-2-22i2i−2i−2i200-2-202000-2200−2i2i-222i−2i0000−2i2i−22−22−22−220000000−i2i2−i2i200000000i2−i22−2i2−i22−20000000000
χ532-22-222-2-22i2i−2i−2i-200220-20002-200−2i2i-22−2i2i00002i−2ii2−i2i2−i2−i2i2−i2i20000000−222−2000000002−2−i2i2−22i2−i20000000000
χ542-22-222-2-22i2i−2i−2i-200220-20002-200−2i2i-22−2i2i00002i−2i−i2i2−i2i2i2−i2i2−i200000002−2−2200000000−22i2−i22−2−i2i20000000000
χ552-22-222-2-22i2i−2i−2i-200220-2000-22002i−2i2-2−2i2i0000−2i2ii2−i2i2−i2−i2i2−i2i20000000−222−200000000−22i2−i22−2−i2i20000000000
χ562-22-222-2-22i2i−2i−2i-200220-2000-22002i−2i2-2−2i2i0000−2i2i−i2i2−i2i2i2−i2i2−i200000002−2−22000000002−2−i2i2−22i2−i20000000000
χ572-22-222-2-2−2i−2i2i2i200-2-2020002-200−2i2i2-2−2i2i0000−2i2i2−22−22−22−20000000−i2i2−i2i200000000−i2i22−2−i2i22−20000000000
χ582-22-222-2-2−2i−2i2i2i200-2-2020002-200−2i2i2-2−2i2i0000−2i2i−22−22−22−220000000i2−i2i2−i200000000i2−i2−22i2−i2−220000000000
χ592-22-222-2-2−2i−2i2i2i200-2-202000-22002i−2i-22−2i2i00002i−2i2−22−22−22−20000000−i2i2−i2i200000000i2−i2−22i2−i2−220000000000
χ602-22-222-2-2−2i−2i2i2i200-2-202000-22002i−2i-22−2i2i00002i−2i−22−22−22−220000000i2−i2i2−i200000000−i2i22−2−i2i22−20000000000
χ612-22-222-2-2−2i−2i2i2i-200220-20002-2002i−2i-222i−2i0000−2i2ii2−i2i2−i2−i2i2−i2i200000002−2−2200000000−22−i2i22−2i2−i20000000000
χ622-22-222-2-2−2i−2i2i2i-200220-20002-2002i−2i-222i−2i0000−2i2i−i2i2−i2i2i2−i2i2−i20000000−222−2000000002−2i2−i2−22−i2i20000000000
χ632-22-222-2-2−2i−2i2i2i-200220-2000-2200−2i2i2-22i−2i00002i−2ii2−i2i2−i2−i2i2−i2i200000002−2−22000000002−2i2−i2−22−i2i20000000000
χ642-22-222-2-2−2i−2i2i2i-200220-2000-2200−2i2i2-22i−2i00002i−2i−i2i2−i2i2i2−i2i2−i20000000−222−200000000−22−i2i22−2i2−i20000000000
χ65444-4-4-44-40000400-440-4000000000000000000022−22−222222−22−22220000000000000000000000000000000000000
χ66444-4-4-44-40000400-440-40000000000000000000−222222−22−222222−220000000000000000000000000000000000000
χ67444-4-4-44-40000-4004-40400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000
χ68444-4-4-44-40000-4004-4040000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000
χ6944-4-44-4-444-44-404400-40-40000000000004-40000000000000000000000000000000000000000000000000
χ7044-4-44-4-444-44-40-4-400404000000000000-440000000000000000000000000000000000000000000000000
χ7144-4-44-4-44-44-4404400-40-4000000000000-440000000000000000000000000000000000000000000000000
χ7244-4-44-4-44-44-440-4-4004040000000000004-40000000000000000000000000000000000000000000000000
χ734-444-4-4-4400004-444-44-4-40000-44000000000000000000000000000000000000000000000000000000000
χ744-444-4-4-440000-44-4-44-4440000-44000000000000000000000000000000000000000000000000000000000
χ754-4-444-44-44i−4i−4i4i000000004-40000000000004i−4i00000000000000000000000000000000000000000000000
χ764-4-444-44-44i−4i−4i4i00000000-44000000000000−4i4i00000000000000000000000000000000000000000000000
χ774-4-444-44-4−4i4i4i−4i000000004-4000000000000−4i4i00000000000000000000000000000000000000000000000
χ784-4-444-44-4−4i4i4i−4i00000000-440000000000004i−4i00000000000000000000000000000000000000000000000
χ794-4-4-4-4444000004-40040-400000000000000000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ804-4-4-4-4444000004-40040-40000000000000000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ814-4-4-4-444400000-4400-404000000000000000000000000000000000000022−22−22220000000000000000000000
χ824-4-4-4-444400000-4400-4040000000000000000000000000000000000000−222222−220000000000000000000000
χ8388-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000

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