Finite Group Databasebeta

← Group #150310

Character table — Group #150310

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112244444488888888881616161616161616161111224444448888888888161616161616161616
order12222244444444888888884448888882222224444444488888888444888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1
χ411111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111
χ51111111-1-11-1-1-1-1iiii−i−i−i−i111-1-1ii−i−i1111111-1-11-1-1-1-1iiii−i−i−i−i111-1-1ii−i−i
χ61111111-1-11-1-1-1-1iiii−i−i−i−i1-1-111−i−iii1111111-1-11-1-1-1-1iiii−i−i−i−i1-1-111−i−iii
χ71111111-1-11-1-1-1-1−i−i−i−iiiii111-1-1−i−iii1111111-1-11-1-1-1-1−i−i−i−iiiii111-1-1−i−iii
χ81111111-1-11-1-1-1-1−i−i−i−iiiii1-1-111ii−i−i1111111-1-11-1-1-1-1−i−i−i−iiiii1-1-111ii−i−i
χ9222222222222-2-200000000-200000000222222222222-2-200000000-200000000
χ102222222-2-22-2-22200000000-2000000002222222-2-22-2-22200000000-200000000
χ1122-2-2-22222-2-2-20000000000000002−22−222-2-2-22222-2-2-20000000000000002−22−2
χ1222-2-2-22222-2-2-2000000000000000−22−2222-2-2-22222-2-2-2000000000000000−22−22
χ1322-2-2-222-2-2-222000000000000000i2−i2−i2i222-2-2-222-2-2-222000000000000000i2−i2−i2i2
χ1422-2-2-222-2-2-222000000000000000−i2i2i2−i222-2-2-222-2-2-222000000000000000−i2i2i2−i2
χ1522-2-2-22-2002002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000022-2-2-22-2002002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000
χ1622-2-2-22-2002002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000022-2-2-22-2002002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000
χ1722-2-2-22-200200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000022-2-2-22-200200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000
χ1822-2-2-22-200200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000022-2-2-22-200200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000
χ19444444-400-4000000000000000000000444444-400-4000000000000000000000
χ204444-4-4000000000000000002-20000004444-4-4000000000000000002-2000000
χ214444-4-400000000000000000-220000004444-4-400000000000000000-22000000
χ2244-4-44-400000000000000000002-2000044-4-44-400000000000000000002-20000
χ2344-4-44-40000000000000000000-22000044-4-44-40000000000000000000-220000
χ244-44-40002i−2i02i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000004-44-40002i−2i02i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000
χ254-44-40002i−2i02i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000004-44-40002i−2i02i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000
χ264-44-4000−2i2i0−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000004-44-4000−2i2i0−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000
χ274-44-4000−2i2i0−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000004-44-4000−2i2i0−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000
χ284-4-440002i−2i0−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000004-4-440002i−2i0−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000
χ294-4-440002i−2i0−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000004-4-440002i−2i0−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000
χ304-4-44000−2i2i02i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000004-4-44000−2i2i02i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000
χ314-4-44000−2i2i02i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000004-4-44000−2i2i02i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000
χ321111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3311111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ3411111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11111
χ3511111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-1
χ361111111-1-11-1-1-1-1iiii−i−i−i−i111-1-1ii−i−i-1-1-1-1-1-1-111-11111−i−i−i−iiiii-1-1-111−i−iii
χ371111111-1-11-1-1-1-1iiii−i−i−i−i1-1-111−i−iii-1-1-1-1-1-1-111-11111−i−i−i−iiiii-111-1-1ii−i−i
χ381111111-1-11-1-1-1-1−i−i−i−iiiii111-1-1−i−iii-1-1-1-1-1-1-111-11111iiii−i−i−i−i-1-1-111ii−i−i
χ391111111-1-11-1-1-1-1−i−i−i−iiiii1-1-111ii−i−i-1-1-1-1-1-1-111-11111iiii−i−i−i−i-111-1-1−i−iii
χ40222222222222-2-200000000-200000000-2-2-2-2-2-2-2-2-2-2-2-22200000000200000000
χ412222222-2-22-2-22200000000-200000000-2-2-2-2-2-2-222-222-2-200000000200000000
χ4222-2-2-22222-2-2-20000000000000002−22−2-2-2222-2-2-2-2222000000000000000−22−22
χ4322-2-2-22222-2-2-2000000000000000−22−22-2-2222-2-2-2-22220000000000000002−22−2
χ4422-2-2-222-2-2-222000000000000000i2−i2−i2i2-2-2222-2-2222-2-2000000000000000−i2i2i2−i2
χ4522-2-2-222-2-2-222000000000000000−i2i2i2−i2-2-2222-2-2222-2-2000000000000000i2−i2−i2i2
χ4622-2-2-22-2002002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000-2-2222-2200-200−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000
χ4722-2-2-22-2002002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000-2-2222-2200-200−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000
χ4822-2-2-22-200200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000-2-2222-2200-2002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000
χ4922-2-2-22-200200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000-2-2222-2200-2002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000
χ50444444-400-4000000000000000000000-4-4-4-4-4-44004000000000000000000000
χ514444-4-4000000000000000002-2000000-4-4-4-44400000000000000000-22000000
χ524444-4-400000000000000000-22000000-4-4-4-444000000000000000002-2000000
χ5344-4-44-400000000000000000002-20000-4-444-440000000000000000000-220000
χ5444-4-44-40000000000000000000-220000-4-444-4400000000000000000002-20000
χ554-44-40002i−2i02i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000-44-44000−2i2i0−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000
χ564-44-40002i−2i02i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000-44-44000−2i2i0−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000
χ574-44-4000−2i2i0−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000-44-440002i−2i02i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000
χ584-44-4000−2i2i0−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000-44-440002i−2i02i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000
χ594-4-440002i−2i0−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000-444-4000−2i2i02i−2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000
χ604-4-440002i−2i0−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000-444-4000−2i2i02i−2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000
χ614-4-44000−2i2i02i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000-444-40002i−2i0−2i2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000
χ624-4-44000−2i2i02i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000-444-40002i−2i0−2i2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000

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