Finite Group Databasebeta

← Group #10883520

Character table — Group #10883520

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order1222223444466666888812121212242424242224446688121224242424242444446688121224242424244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-111-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-11111-111-1-1-1-1
χ4111111111111111111111111111111-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11-1-1-1-11-1-11111
χ51111111111111111111111111111-1-11-1-111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1
χ61111111111111111111111111111-1-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-111-1-1
χ91111111111111111-1-1-1-11111-1-1-1-1111-1-1111-1-111-1-1-1-1-1-11111111-1-1-111-1-1111-1-11-1-1-1-11-1
χ101111111111111111-1-1-1-11111-1-1-1-1111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-111-11111-11
χ111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111111111-11-1-1-1-111-111-1-1-1-1-111-11
χ121111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-11-1-1-1-1111-1-111111-1-11-1
χ131111111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1111-1-1111-1-1111-1-1-1-1-11
χ141111111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-111-1-1-111111-1
χ151111111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-111-1-1-1-111111111-1-11-11111-1-1-1-1-111-1-1-1111-1
χ161111111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-1-1-11-11111-1-1111-1-1111-1-1-11
χ172222222-2-2-2-2222220000-2-2-2-20000000000002i−2i00002i2i−2i−2i22-2-20000000000000000002i−2i00
χ182222222-2-2-2-2222220000-2-2-2-20000000000002i−2i00002i2i−2i−2i-2-222000000000000000000−2i2i00
χ192222222-2-2-2-2222220000-2-2-2-2000000000000−2i2i0000−2i−2i2i2i22-2-2000000000000000000−2i2i00
χ202222222-2-2-2-2222220000-2-2-2-2000000000000−2i2i0000−2i−2i2i2i-2-2220000000000000000002i−2i00
χ21222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-122-1-1-1-1-1-1-1-10000-1-122-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-122-222-211-2-211-1-111110000-1-1-2-2-1-11111000000000000
χ23222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-22-2-22-1-122-1-1-1-1-1-1-1-1000011-2-2111111000000000000
χ24222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-211-2-211-1-111110000112211-1-1-1-1000000000000
χ25222222-12222-1-1-1-1-1-2-2-2-2-1-1-1-11111222-2-22-1-1-2-2-1-11111110000-1-12-211-1-111000000000000
χ26222222-12222-1-1-1-1-1-2-2-2-2-1-1-1-1111122-2-2-2-211221111-1-1-1-10000-1-1-221111-1-1000000000000
χ27222222-12222-1-1-1-1-1-2-2-2-2-1-1-1-11111-2-22222-1-1-2-2-1-1111111000011-22-1-111-1-1000000000000
χ28222222-12222-1-1-1-1-1-2-2-2-2-1-1-1-11111-2-2-222-211221111-1-1-1-10000112-2-1-1-1-111000000000000
χ292222-2-222-2-22222-2-222-2-22-2-222222000000000000-2-200002-22-200000000000000002-20000
χ302222-2-222-2-22222-2-222-2-22-2-222222000000000000-2-20000-22-220000000000000000-220000
χ312222-2-222-2-22222-2-2-2-2222-2-22-2-2-2-20000000000002200002-22-20000000000000000-220000
χ322222-2-222-2-22222-2-2-2-2222-2-22-2-2-2-2000000000000220000-22-2200000000000000002-20000
χ332222-2-22-222-2222-2-20000-222-2000000200-22200-2-20000002-2-22000000000020000-2000000
χ342222-2-22-222-2222-2-20000-222-2000000200-22200-2-2000000-222-20000000000-200002000000
χ352222-2-22-222-2222-2-20000-222-2000000-2002-2-200220000002-2-220000000000-200002000000
χ362222-2-22-222-2222-2-20000-222-2000000-2002-2-20022000000-222-2000000000020000-2000000
χ372-22-22-2222-2-2-22-22-22i−2i2i−2i22-2-22i2i−2i−2i0000000000002i−2i00000000000000000002i−2i2-20000000
χ382-22-22-2222-2-2-22-22-22i−2i2i−2i22-2-22i2i−2i−2i0000000000002i−2i0000000000000000000−2i2i-220000000
χ392-22-22-2222-2-2-22-22-2−2i2i−2i2i22-2-2−2i−2i2i2i000000000000−2i2i00000000000000000002i−2i-220000000
χ402-22-22-2222-2-2-22-22-2−2i2i−2i2i22-2-2−2i−2i2i2i000000000000−2i2i0000000000000000000−2i2i2-20000000
χ412-22-2-2222-22-2-22-2-222i−2i−2i2i2-22-22i2i−2i−2i2-202i−2i0000000−2i2i000000002-2002i−2i0000000000000000
χ422-22-2-2222-22-2-22-2-222i−2i−2i2i2-22-22i2i−2i−2i-220−2i2i0000000−2i2i00000000-2200−2i2i0000000000000000
χ432-22-2-2222-22-2-22-2-22−2i2i2i−2i2-22-2−2i−2i2i2i2-20−2i2i00000002i−2i000000002-200−2i2i0000000000000000
χ442-22-2-2222-22-2-22-2-22−2i2i2i−2i2-22-2−2i−2i2i2i-2202i−2i00000002i−2i00000000-22002i−2i0000000000000000
χ452-22-2-22-12-22-21-111-12i−2i−2i2i-11-11−i−iii2-202i−2i0−i3i300−i3i3i−i3−33−30000-1100−ii−i3i33−3000000000000
χ462-22-2-22-12-22-21-111-12i−2i−2i2i-11-11−i−iii2-202i−2i0i3−i300i3−i3i−i−33−330000-1100−iii3−i3−33000000000000
χ472-22-2-22-12-22-21-111-12i−2i−2i2i-11-11−i−iii-220−2i2i0−i3i300−i3i3i−i3−33−300001-100i−ii3−i3−33000000000000
χ482-22-2-22-12-22-21-111-12i−2i−2i2i-11-11−i−iii-220−2i2i0i3−i300i3−i3i−i−33−3300001-100i−i−i3i33−3000000000000
χ492-22-2-22-12-22-21-111-1−2i2i2i−2i-11-11ii−i−i2-20−2i2i0−i3i300−i3i3−ii−33−330000-1100i−i−i3i3−33000000000000
χ502-22-2-22-12-22-21-111-1−2i2i2i−2i-11-11ii−i−i2-20−2i2i0i3−i300i3−i3−ii3−33−30000-1100i−ii3−i33−3000000000000
χ512-22-2-22-12-22-21-111-1−2i2i2i−2i-11-11ii−i−i-2202i−2i0−i3i300−i3i3−ii−33−3300001-100−iii3−i33−3000000000000
χ522-22-2-22-12-22-21-111-1−2i2i2i−2i-11-11ii−i−i-2202i−2i0i3−i300i3−i3−ii3−33−300001-100−ii−i3i3−33000000000000
χ53444444-2-4-4-4-4-2-2-2-2-2000022220000000000004i−4i0000−2i−2i2i2i00000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-2-200002222000000000000−4i4i00002i2i−2i−2i00000000000000000000000000
χ554444-4-4-24-4-44-2-2-22244-4-4-222-2-2-2-2-200000000000022000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-222-4-444-222-22222000000000000-2-2000000000000000000000000000000
χ574444-4-4-2-444-4-2-2-22200002-2-22000000400-4-2-2002200000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-22200002-2-22000000-40042200-2-200000000000000000000000000000000
χ594-44-44-44-4-444-44-44-40000-4-444000000000000000000000000000000000000000000000000
χ604-44-44-4-244-4-42-22-224i−4i4i−4i-2-222−2i−2i2i2i000000000000−2i2i000000000000000000000000000000
χ614-44-44-4-244-4-42-22-22−4i4i−4i4i-2-2222i2i−2i−2i0000000000002i−2i000000000000000000000000000000
χ624-44-44-4-2-4-4442-22-22000022-2-20000000000−2i32i3002i3−2i300000000000000000000000000000000
χ634-44-44-4-2-4-4442-22-22000022-2-200000000002i3−2i300−2i32i300000000000000000000000000000000
χ644-44-4-444-44-44-44-4-440000-44-44000000000000000000000000000000000000000000000000
χ654-44-4-44-2-44-442-222-200002-22-2000000000000000000−2i32i32i3−2i300000000000000000000000000
χ664-44-4-44-2-44-442-222-200002-22-20000000000000000002i3−2i3−2i32i300000000000000000000000000
χ6788-8-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000-444000000000026−2626−2600000000000000000000000000000000000000000000
χ6988-8-800-40000-4440000000000−2626−262600000000000000000000000000000000000000000000
χ708-8-880080000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-8800-4000044-400000000002i6−2i6−2i62i600000000000000000000000000000000000000000000
χ728-8-8800-4000044-40000000000−2i62i62i6−2i600000000000000000000000000000000000000000000

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