Finite Group Databasebeta

← Group #10909569

Character table — Group #10909569

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222224444444444448888888888888888888121216161616161616161616242424242424242424484848
order1222223444466666881212121224242424222444668881212242424242424884466121212121212222444888488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-111-1-1-11-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-111111-11-1
χ41111111111111111111111111111-111-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-11-11
χ511111111111111111111111111-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11
χ611111111111111111111111111-1-11-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1
χ711111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-11111-1-11111-1-1-111-1111-1-11-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-111-1-11111-1-11-1-11-1-1-111-111
χ91111111111111111-1-11111-1-1-1-11-111-1111-1-1-111-1-1-1-1-1-1111-11-111-1-11-11111-1-11-1-1-11-1
χ101111111111111111-1-11111-1-1-1-11-111-1111-1-1-111-1-1-1-1-1-1-1-11-11-111-1-11-1-1-1-1-111-1111-11
χ111111111111111111-1-11111-1-1-1-11-1-11-1-1-1-1-111-1-1-1-1111111-111-1-1-1111-1-1-1-1-1-1-11-1-1111
χ121111111111111111-1-11111-1-1-1-11-1-11-1-1-1-1-111-1-1-1-11111-1-1-111-1-1-1111-1111111-111-1-1-1
χ131111111111111111-1-11111-1-1-1-1-111-11111-1-1-111-1-1-1-1-1-111-11-11-1-111-111-1-11-1-11111-1-1
χ141111111111111111-1-11111-1-1-1-1-111-11111-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111-11-111-111-1-1-1-111
χ151111111111111111-1-11111-1-1-1-1-11-1-11-1-1-1-111-1-1-1-11111111-1-1111-1-1-11-111-1-1-1111-1-11
χ161111111111111111-1-11111-1-1-1-1-11-1-11-1-1-1-111-1-1-1-11111-1-11-1-1111-1-1-111-1-1111-1-1-111-1
χ17222222-12222-1-1-1-1-122-1-1-1-1-1-1-1-1222222-1-1222-1-1-1-1-1-1-1-10022-1-1-1-1-1-1-1-1000000000000
χ18222222-12222-1-1-1-1-122-1-1-1-1-1-1-1-122-222-2112-2-211-1-1111100-2-2-1-11111-1-1000000000000
χ19222222-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-2-22-2-22-1-1222-1-1-1-1-1-1-1-100-2-211111111000000000000
χ20222222-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2112-2-211-1-11111002211-1-1-1-111000000000000
χ21222222-12222-1-1-1-1-1-2-2-1-1-1-111112-222-22-1-1-2-2-2-1-1111111002-2-11-1-111-11000000000000
χ22222222-12222-1-1-1-1-1-2-2-1-1-1-111112-2-22-2-211-2221111-1-1-1-100-22-1111-1-1-11000000000000
χ23222222-12222-1-1-1-1-1-2-2-1-1-1-11111-222-222-1-1-2-2-2-1-111111100-221-111-1-11-1000000000000
χ24222222-12222-1-1-1-1-1-2-2-1-1-1-11111-22-2-22-211-2221111-1-1-1-1002-21-1-1-1111-1000000000000
χ252222-2-2222-2-2222-2-2222-2-2222222-20-22000-20000-2-2000000002-20000-22000000000000
χ262222-2-2222-2-2222-2-2222-2-222222-2202-2000-20000-2-200000000-2200002-2000000000000
χ272222-2-2222-2-2222-2-2-2-22-2-22-2-2-2-2220-2-2000200002200000000220000-2-2000000000000
χ282222-2-2222-2-2222-2-2-2-22-2-22-2-2-2-2-2-2022000200002200000000-2-2000022000000000000
χ292222-2-22-2-222222-2-200-222-2000000200-222000-2-2000000220000000000200-200-200000
χ302222-2-22-2-222222-2-200-222-2000000200-222000-2-2000000-2-20000000000-200200200000
χ312222-2-22-2-222222-2-200-222-2000000-2002-2-200022000000220000000000-200200-200000
χ322222-2-22-2-222222-2-200-222-2000000-2002-2-200022000000-2-20000000000200-200200000
χ332222-2-2-122-2-2-1-1-11122-111-1-1-1-1-12-20-220−i3i3-200−i3i311−i3−i3i3i30000-11−i3i3−i3i31-1000000000000
χ342222-2-2-122-2-2-1-1-11122-111-1-1-1-1-12-20-220i3−i3-200i3−i311i3i3−i3−i30000-11i3−i3i3−i31-1000000000000
χ352222-2-2-122-2-2-1-1-11122-111-1-1-1-1-1-2202-20−i3i3-200−i3i311−i3−i3i3i300001-1i3−i3i3−i3-11000000000000
χ362222-2-2-122-2-2-1-1-11122-111-1-1-1-1-1-2202-20i3−i3-200i3−i311i3i3−i3−i300001-1−i3i3−i3i3-11000000000000
χ372222-2-2-122-2-2-1-1-111-2-2-111-11111220-2-20−i3i3200−i3i3-1-1i3i3−i3−i30000-1-1−i3i3i3−i311000000000000
χ382222-2-2-122-2-2-1-1-111-2-2-111-11111220-2-20i3−i3200i3−i3-1-1−i3−i3i3i30000-1-1i3−i3−i3i311000000000000
χ392222-2-2-122-2-2-1-1-111-2-2-111-11111-2-20220−i3i3200−i3i3-1-1i3i3−i3−i3000011i3−i3−i3i3-1-1000000000000
χ402222-2-2-122-2-2-1-1-111-2-2-111-11111-2-20220i3−i3200i3−i3-1-1−i3−i3i3i3000011−i3i3i3−i3-1-1000000000000
χ412-22-22-22-222-2-2-222-20022-2-200000000000002i−2i00002i−2i2i−2i00000000000002-200002i−2i000
χ422-22-22-22-222-2-2-222-20022-2-200000000000002i−2i00002i−2i2i−2i0000000000000-220000−2i2i000
χ432-22-22-22-222-2-2-222-20022-2-20000000000000−2i2i0000−2i2i−2i2i00000000000002-20000−2i2i000
χ442-22-22-22-222-2-2-222-20022-2-20000000000000−2i2i0000−2i2i−2i2i0000000000000-2200002i−2i000
χ454444444-4-4-4-44444400-4-4-4-400000000000000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2-2-20022220000000000−2i32i30002i3−2i3000000000000000000000000000000
χ47444444-2-4-4-4-4-2-2-2-2-200222200000000002i3−2i3000−2i32i3000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-222002-2-22000000400-4-2-200022000000000000000000000000000000
χ494444-4-4-2-4-444-2-2-222002-2-22000000-400422000-2-2000000000000000000000000000000
χ5044-4-400400004-4-400−2i22i20000−2i2−2i22i22i2000000000000000000022−22000000000000002i−2i000000
χ5144-4-400400004-4-400−2i22i20000−2i2−2i22i22i20000000000000000000−222200000000000000−2i2i000000
χ5244-4-400400004-4-4002i2−2i200002i22i2−2i2−2i2000000000000000000022−2200000000000000−2i2i000000
χ5344-4-400400004-4-4002i2−2i200002i22i2−2i2−2i20000000000000000000−2222000000000000002i−2i000000
χ544-44-44-444-4-44-4-444-400-4-44400000000000000000000000000000000000000000000000
χ554-44-44-4-24-4-4422-2-220022-2-2−2i32i3−2i32i30000000000000−2i32i30000000000000000000000000000
χ564-44-44-4-24-4-4422-2-220022-2-22i3−2i32i3−2i300000000000002i3−2i30000000000000000000000000000
χ574-44-44-4-2-444-422-2-2200-2-22200000000000004i−4i0000−2i2i−2i2i000000000000000000000000
χ584-44-44-4-2-444-422-2-2200-2-2220000000000000−4i4i00002i−2i2i−2i000000000000000000000000
χ594-44-4-4444-44-4-4-44-4400-44-4400000000000000000000000000000000000000000000000
χ604-44-4-444-44-44-4-44-44004-44-400000000000000000000000000000000000000000000000
χ614-44-4-44-24-44-422-22-2002-22-2−2i32i3−2i32i300000000000002i3−2i30000000000000000000000000000
χ624-44-4-44-24-44-422-22-2002-22-22i3−2i32i3−2i30000000000000−2i32i30000000000000000000000000000
χ634-44-4-44-2-44-4422-22-200-22-22000000000000000000023−23−2323000000000000000000000000
χ644-44-4-44-2-44-4422-22-200-22-220000000000000000000−232323−23000000000000000000000000
χ6588-8-800-40000-44400−4i24i200002i22i2−2i2−2i20000000000000000000000000000000000000000000
χ6688-8-800-40000-444004i2−4i20000−2i2−2i22i22i20000000000000000000000000000000000000000000
χ678-8-880080000-88-80000000000000000000000000000000000000000000000000000000
χ688-8-8800-400004-440000000026−26−26260000000000000000000000000000000000000000000
χ698-8-8800-400004-4400000000−262626−260000000000000000000000000000000000000000000

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