Finite Group Databasebeta

← Group #10827238

Character table — Group #10827238

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222224444444444888888888888888888888888121212121616161616161616242424242424242424244848
order122222344446664444661212121224444444661212121212121212121212121212224488121224242424222444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-11-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1
χ4111111111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111
χ5111111111111111111111111-1-1-111-111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-111-1-111-111-1-1
χ6111111111111111111111111-1-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1-111-1-11-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-111-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1111-1-1
χ911111111111111-1-1-1-11111111-1111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111-11111-1-1-1111-1-1-11-1-11-1
χ1011111111111111-1-1-1-11111111-1111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11111-1-11-1-1-1111-111-11
χ1111111111111111-1-1-1-11111111-11-1-1-11111-1-1-1-1-1-1-1-11111111111-11-1-1-1-111-1-1-11-1-1-1111-11
χ1211111111111111-1-1-1-11111111-11-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-111111-1111-1-1-11-1
χ1311111111111111-1-1-1-1111111-11-1111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1111-1-111111-11-1-1-1-1-1-11
χ1411111111111111-1-1-1-1111111-11-1111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-11-1111111-1
χ1511111111111111-1-1-1-1111111-11-1-1-1111-1-111-1-1-1-111-1-1111111111-1-1-111-1-11-1-1-11-1-1-1111-1
χ1611111111111111-1-1-1-1111111-11-1-1-1111-1-111-1-1-1-111-1-11111-1-1-1-11-1-1-111-1-1-1111-1111-1-1-11
χ172222222-2-2-2-222222-2-222-2-2-2-200000000000022-2-20000000022-2-200000000000002-200000
χ182222222-2-2-2-222222-2-222-2-2-2-200000000000022-2-200000000-2-2220000000000000-2200000
χ192222222-2-2-2-2222-2-22222-2-2-2-2000000000000-2-2220000000022-2-20000000000000-2200000
χ202222222-2-2-2-2222-2-22222-2-2-2-2000000000000-2-22200000000-2-22200000000000002-200000
χ21222222-12222-1-1-12222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-1222-2-22-2-2-1-1-1-1-1-1-1-1-1-1-1-111110000-2-2111111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-2-2-222-2221111-1-1-1-11111-1-1-1-10000-2-2-1-11111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-11111111100002211-1-1-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-12-2222-2-2-2-1-111111111-1-1111100002-2-1-1-1-111000000000000
χ26222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-12-22-2-2-222-1-111111111-1-1-1-1-1-10000-221111-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-22-2222-2-211-1-11111-1-11111110000-22-1-111-1-1000000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-22-2-2-222211-1-11111-1-111-1-1-1-100002-211-1-111000000000000
χ292222-2-222-22-22220000-2-22-22-202000-20000220000-2-20000002-22-2000000002000-20000000
χ302222-2-222-22-22220000-2-22-22-202000-20000220000-2-2000000-22-2200000000-200020000000
χ312222-2-222-22-22220000-2-22-22-20-200020000-2-20000220000002-22-200000000-200020000000
χ322222-2-222-22-22220000-2-22-22-20-200020000-2-2000022000000-22-22000000002000-20000000
χ332222-2-22-22-222220000-2-2-22-2220-2000002200000000-2-200002-2-22000000000002000-20000
χ342222-2-22-22-222220000-2-2-22-2220-2000002200000000-2-20000-222-200000000000-200020000
χ352222-2-22-22-222220000-2-2-22-22-20200000-2-2000000002200002-2-2200000000000-200020000
χ362222-2-22-22-222220000-2-2-22-22-20200000-2-200000000220000-222-2000000000002000-20000
χ372-22-22-222-2-22-2-222i−2i2i−2i2-2-222-20000000000002i−2i2i−2i0000000000000000000002-2000002i−2i00
χ382-22-22-222-2-22-2-222i−2i2i−2i2-2-222-20000000000002i−2i2i−2i000000000000000000000-2200000−2i2i00
χ392-22-22-222-2-22-2-22−2i2i−2i2i2-2-222-2000000000000−2i2i−2i2i0000000000000000000002-200000−2i2i00
χ402-22-22-222-2-22-2-22−2i2i−2i2i2-2-222-2000000000000−2i2i−2i2i000000000000000000000-22000002i−2i00
χ412-22-22-22-222-2-2-222i−2i−2i2i2-22-2-220002-202i−2i00002i−2i−2i2i00002i2i−2i−2i0000002-20000000000000000
χ422-22-22-22-222-2-2-222i−2i−2i2i2-22-2-22000-220−2i2i00002i−2i−2i2i0000−2i−2i2i2i000000-220000000000000000
χ432-22-22-22-222-2-2-22−2i2i2i−2i2-22-2-220002-20−2i2i0000−2i2i2i−2i0000−2i−2i2i2i0000002-20000000000000000
χ442-22-22-22-222-2-2-22−2i2i2i−2i2-22-2-22000-2202i−2i0000−2i2i2i−2i00002i2i−2i−2i000000-220000000000000000
χ452-22-22-2-1-222-211-12i−2i−2i2i-11-111-10002-202i−2i−i3i33−3−iii−i3−3−i3i3−i−iii000000-11−i3i33−3000000000000
χ462-22-22-2-1-222-211-12i−2i−2i2i-11-111-10002-202i−2ii3−i3−33−iii−i−33i3−i3−i−iii000000-11i3−i3−33000000000000
χ472-22-22-2-1-222-211-12i−2i−2i2i-11-111-1000-220−2i2i−i3i33−3−iii−i3−3−i3i3ii−i−i0000001-1i3−i3−33000000000000
χ482-22-22-2-1-222-211-12i−2i−2i2i-11-111-1000-220−2i2ii3−i3−33−iii−i−33i3−i3ii−i−i0000001-1−i3i33−3000000000000
χ492-22-22-2-1-222-211-1−2i2i2i−2i-11-111-10002-20−2i2i−i3i3−33i−i−ii−33−i3i3ii−i−i000000-11−i3i3−33000000000000
χ502-22-22-2-1-222-211-1−2i2i2i−2i-11-111-10002-20−2i2ii3−i33−3i−i−ii3−3i3−i3ii−i−i000000-11i3−i33−3000000000000
χ512-22-22-2-1-222-211-1−2i2i2i−2i-11-111-1000-2202i−2i−i3i3−33i−i−ii−33−i3i3−i−iii0000001-1i3−i33−3000000000000
χ522-22-22-2-1-222-211-1−2i2i2i−2i-11-111-1000-2202i−2ii3−i33−3i−i−ii3−3i3−i3−i−iii0000001-1−i3i3−33000000000000
χ53444444-2-4-4-4-4-2-2-244-4-4-2-22222000000000000-2-22200000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-4-444-2-2222200000000000022-2-200000000000000000000000000000000
χ554444-4-4-24-44-4-2-2-2000022-22-2204000-40000-2-2000022000000000000000000000000000000
χ564444-4-4-24-44-4-2-2-2000022-22-220-400040000220000-2-2000000000000000000000000000000
χ574444-4-4-2-44-44-2-2-20000222-22-240-400000-2-200000000220000000000000000000000000000
χ584444-4-4-2-44-44-2-2-20000222-22-2-404000002200000000-2-20000000000000000000000000000
χ594-44-44-4-24-4-4422-24i−4i4i−4i-222-2-22000000000000−2i2i−2i2i00000000000000000000000000000000
χ604-44-44-4-24-4-4422-2−4i4i−4i4i-222-2-220000000000002i−2i2i−2i00000000000000000000000000000000
χ614-44-4-44444-4-4-4-440000-44-4-444000000000000000000000000000000000000000000000000
χ624-44-4-444-4-444-4-440000-4444-4-4000000000000000000000000000000000000000000000000
χ634-44-4-44-244-4-422-200002-222-2-200000000−2i32i3000000002i3−2i30000000000000000000000000000
χ644-44-4-44-244-4-422-200002-222-2-2000000002i3−2i300000000−2i32i30000000000000000000000000000
χ654-44-4-44-2-4-44422-200002-2-2-222000000000023−230000−2323000000000000000000000000000000
χ664-44-4-44-2-4-44422-200002-2-2-2220000000000−2323000023−23000000000000000000000000000000
χ6788-8-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000-444000000000000000000000000000000−2i32i3−2i32i3000000000000000000000000
χ6988-8-800-40000-4440000000000000000000000000000002i3−2i32i3−2i3000000000000000000000000
χ708-8-880080000-88-80000000000000000000000000000000000000000000000000000000000
χ718-8-8800-400004-4400000000000000000000000000000023−23−2323000000000000000000000000
χ728-8-8800-400004-44000000000000000000000000000000−232323−23000000000000000000000000

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