Finite Group Databasebeta

← Group #150232

Character table — Group #150232

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112244444488888888881616161616161616161111224444448888888888161616161616161616
order12222244444444888888882448888882222224444444488888888244888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-11-1-1-1-1-1-1-11111111111111111111111-11-1-1-1-1-1-1-1
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
χ411111111111111-1-1-1-1-1-1-1-1-11-1-1-1111111111111111111-1-1-1-1-1-1-1-1-11-1-1-11111
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−i-11-111−i−iii1111111-1-11-1-1-1-1iiii−i−i−i−i-11-111−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−iiiii-11-111ii−i−i1111111-1-11-1-1-1-1−i−i−i−iiiii-11-111ii−i−i
χ9222222222222-2-2000000000-20000000222222222222-2-2000000000-20000000
χ102222222-2-22-2-222000000000-200000002222222-2-22-2-222000000000-20000000
χ112-2-22-22200-2002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000002-2-22-22200-2002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000
χ122-2-22-22200-2002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000002-2-22-22200-2002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000
χ132-2-22-22200-200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000002-2-22-22200-200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000
χ142-2-22-22200-200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000002-2-22-22200-200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000
χ152-2-22-22-2222-2-2000000000000000i2−i2i2−i22-2-22-22-2222-2-2000000000000000i2−i2i2−i2
χ162-2-22-22-2222-2-2000000000000000−i2i2−i2i22-2-22-22-2222-2-2000000000000000−i2i2−i2i2
χ172-2-22-22-2-2-22220000000000000002−2−222-2-22-22-2-2-22220000000000000002−2−22
χ182-2-22-22-2-2-2222000000000000000−222−22-2-22-22-2-2-2222000000000000000−222−2
χ19444444-400-4000000000000000000000444444-400-4000000000000000000000
χ204444-4-4000000000000000020-20000004444-4-4000000000000000020-2000000
χ214444-4-40000000000000000-2020000004444-4-40000000000000000-202000000
χ2244-4-40002i−2i02i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000044-4-40002i−2i02i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000
χ2344-4-40002i−2i02i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000044-4-40002i−2i02i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000
χ2444-4-4000−2i2i0−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000044-4-4000−2i2i0−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000
χ2544-4-4000−2i2i0−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000044-4-4000−2i2i0−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000
χ264-44-40002i−2i0−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000004-44-40002i−2i0−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000
χ274-44-40002i−2i0−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000004-44-40002i−2i0−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000
χ284-44-4000−2i2i02i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000004-44-4000−2i2i02i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000
χ294-44-4000−2i2i02i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000004-44-4000−2i2i02i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000
χ304-4-444-400000000000000000002i−2i00004-4-444-400000000000000000002i−2i0000
χ314-4-444-40000000000000000000−2i2i00004-4-444-40000000000000000000−2i2i0000
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
χ331111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111
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
χ3511111111111111-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1111-1-1-1-1
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−i-11-111−i−iii-1-1-1-1-1-1-111-11111−i−i−i−iiiii1-11-1-1ii−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−iiiii-11-111ii−i−i-1-1-1-1-1-1-111-11111iiii−i−i−i−i1-11-1-1−i−iii
χ40222222222222-2-2000000000-20000000-2-2-2-2-2-2-2-2-2-2-2-22200000000020000000
χ412222222-2-22-2-222000000000-20000000-2-2-2-2-2-2-222-222-2-200000000020000000
χ422-2-22-22200-2002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000-222-22-2-200200−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000
χ432-2-22-22200-2002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000-222-22-2-200200−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000
χ442-2-22-22200-200−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000-222-22-2-2002002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000
χ452-2-22-22200-200−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000-222-22-2-2002002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000
χ462-2-22-22-2222-2-2000000000000000i2−i2i2−i2-222-22-22-2-2-222000000000000000−i2i2−i2i2
χ472-2-22-22-2222-2-2000000000000000−i2i2−i2i2-222-22-22-2-2-222000000000000000i2−i2i2−i2
χ482-2-22-22-2-2-22220000000000000002−2−22-222-22-2222-2-2-2000000000000000−222−2
χ492-2-22-22-2-2-2222000000000000000−222−2-222-22-2222-2-2-20000000000000002−2−22
χ50444444-400-4000000000000000000000-4-4-4-4-4-44004000000000000000000000
χ514444-4-4000000000000000020-2000000-4-4-4-4440000000000000000-202000000
χ524444-4-40000000000000000-202000000-4-4-4-444000000000000000020-2000000
χ5344-4-40002i−2i02i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000-4-444000−2i2i0−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000
χ5444-4-40002i−2i02i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000-4-444000−2i2i0−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000
χ5544-4-4000−2i2i0−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000-4-4440002i−2i02i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000
χ5644-4-4000−2i2i0−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000-4-4440002i−2i02i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000
χ574-44-40002i−2i0−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000-44-44000−2i2i02i−2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000
χ584-44-40002i−2i0−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000-44-44000−2i2i02i−2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000
χ594-44-4000−2i2i02i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000-44-440002i−2i0−2i2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000
χ604-44-4000−2i2i02i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000-44-440002i−2i0−2i2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000
χ614-4-444-400000000000000000002i−2i0000-444-4-440000000000000000000−2i2i0000
χ624-4-444-40000000000000000000−2i2i0000-444-4-4400000000000000000002i−2i0000

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