Finite Group Databasebeta

← Group #10824921

Character table — Group #10824921

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444666666668888888888888888881616161616161616161616162424242424242424242424242424
order122222344446666612121212444444442244448888888824242424661212121224242424242424444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-11-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111-111-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ51111111111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-111-1-111-1-1-1-1
χ61111111111111111111111111111-1-11-1-111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1111111
χ1111111111111111111111-1-1-1-1-1-1-1-111-111-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111
χ172222222-2-2-2-222222-2-2-2-22222-2-2-2-2000000002i−2i0000000000000000002i−2i0000000000002i−2i
χ182222222-2-2-2-222222-2-2-2-22222-2-2-2-200000000−2i2i000000000000000000−2i2i000000000000−2i2i
χ192222222-2-2-2-222222-2-2-2-2-2-2-2-22222000000002i−2i0000000000000000002i−2i000000000000−2i2i
χ202222222-2-2-2-222222-2-2-2-2-2-2-2-2222200000000−2i2i000000000000000000−2i2i0000000000002i−2i
χ21222222-12222-1-1-1-1-1-1-1-1-10000000022222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222222-12222-1-1-1-1-1-1-1-1-100000000222-2-22-2-2-2-222-2-21111-1-1-1-111-1-1111100000000000000
χ23222222-12222-1-1-1-1-1-1-1-1-10000000022-222-222-2-2-2-2-2-2-1-1-1-1-1-111-1-111111100000000000000
χ24222222-12222-1-1-1-1-1-1-1-1-10000000022-2-2-2-2-2-222-2-2221111-1-1111111-1-1-1-100000000000000
χ25222222-12222-1-1-1-1-1-1-1-1-100000000-2-22222-2-2-2-2-2-222111111-1-1-1-111-1-11100000000000000
χ26222222-12222-1-1-1-1-1-1-1-1-100000000-2-22-2-222222-2-2-2-2-1-1-1-111-1-1111111-1-100000000000000
χ27222222-12222-1-1-1-1-1-1-1-1-100000000-2-2-222-2-2-22222-2-211111111-1-1-1-111-1-100000000000000
χ28222222-12222-1-1-1-1-1-1-1-1-100000000-2-2-2-2-2-222-2-22222-1-1-1-1111111-1-1-1-11100000000000000
χ292222-2-222-2-22222-2-22-2-2222-2-222-2-20000002-200000022-2-200000000000000000000002-200
χ302222-2-222-2-22222-2-22-2-2222-2-222-2-2000000-22000000-2-2220000000000000000000000-2200
χ312222-2-222-2-22222-2-22-2-22-2-222-2-2220000002-200000022-2-20000000000000000000000-2200
χ322222-2-222-2-22222-2-22-2-22-2-222-2-222000000-22000000-2-22200000000000000000000002-200
χ332222-2-22-222-2222-2-2-222-222-2-2-2-22200200-2000000000000002-2000000002-2000000000000
χ342222-2-22-222-2222-2-2-222-222-2-2-2-22200-200200000000000000-2200000000-22000000000000
χ352222-2-22-222-2222-2-2-222-2-2-22222-2-200200-2000000000000002-200000000-22000000000000
χ362222-2-22-222-2222-2-2-222-2-2-22222-2-200-200200000000000000-22000000002-2000000000000
χ372-22-22-2222-2-2-2-222-2-22-222i−2i2i−2i2i−2i2i−2i0002-2000000000000000002-200000000002i−2i00000000
χ382-22-22-2222-2-2-2-222-2-22-222i−2i2i−2i2i−2i2i−2i000-2200000000000000000-220000000000−2i2i00000000
χ392-22-22-2222-2-2-2-222-2-22-22−2i2i−2i2i−2i2i−2i2i0002-2000000000000000002-20000000000−2i2i00000000
χ402-22-22-2222-2-2-2-222-2-22-22−2i2i−2i2i−2i2i−2i2i000-2200000000000000000-2200000000002i−2i00000000
χ412-22-22-22-2-222-2-222-22-22-22i−2i2i−2i−2i2i−2i2i00000000002i−2i0000000000002i−2i00000000002-2000000
χ422-22-22-22-2-222-2-222-22-22-22i−2i2i−2i−2i2i−2i2i0000000000−2i2i000000000000−2i2i0000000000-22000000
χ432-22-22-22-2-222-2-222-22-22-2−2i2i−2i2i2i−2i2i−2i00000000002i−2i0000000000002i−2i0000000000-22000000
χ442-22-22-22-2-222-2-222-22-22-2−2i2i−2i2i2i−2i2i−2i0000000000−2i2i000000000000−2i2i00000000002-2000000
χ452-22-2-2222-22-2-2-22-22-2-2222i−2i−2i2i2i−2i−2i2i2-200000000000000002-20000000000002i−2i0000000000
χ462-22-2-2222-22-2-2-22-22-2-2222i−2i−2i2i2i−2i−2i2i-220000000000000000-22000000000000−2i2i0000000000
χ472-22-2-2222-22-2-2-22-22-2-222−2i2i2i−2i−2i2i2i−2i2-200000000000000002-2000000000000−2i2i0000000000
χ482-22-2-2222-22-2-2-22-22-2-222−2i2i2i−2i−2i2i2i−2i-220000000000000000-220000000000002i−2i0000000000
χ492-22-2-222-22-22-2-22-2222-2-22i−2i−2i2i−2i2i2i−2i0000000000002i−2i0000000000002i−2i00000000002-20000
χ502-22-2-222-22-22-2-22-2222-2-22i−2i−2i2i−2i2i2i−2i000000000000−2i2i000000000000−2i2i0000000000-220000
χ512-22-2-222-22-22-2-22-2222-2-2−2i2i2i−2i2i−2i−2i2i0000000000002i−2i0000000000002i−2i0000000000-220000
χ522-22-2-222-22-22-2-22-2222-2-2−2i2i2i−2i2i−2i−2i2i000000000000−2i2i000000000000−2i2i00000000002-20000
χ53444444-2-4-4-4-4-2-2-2-2-2222200000000000000004i−4i000000000000000000−2i2i00000000000000
χ54444444-2-4-4-4-4-2-2-2-2-222220000000000000000−4i4i0000000000000000002i−2i00000000000000
χ554444-4-4-24-4-44-2-2-222-222-2000000000000004-4000000-2-22200000000000000000000000000
χ564444-4-4-24-4-44-2-2-222-222-200000000000000-4400000022-2-200000000000000000000000000
χ574444-4-4-2-444-4-2-2-2222-2-220000000000400-400000000000000-220000000000000000000000
χ584444-4-4-2-444-4-2-2-2222-2-220000000000-4004000000000000002-20000000000000000000000
χ594-44-44-4-244-4-422-2-222-22-2000000000004-400000000000000000-2200000000000000000000
χ604-44-44-4-244-4-422-2-222-22-200000000000-44000000000000000002-200000000000000000000
χ614-44-44-4-2-4-44422-2-22-22-220000000000000000004i−4i000000000000−2i2i000000000000000000
χ624-44-44-4-2-4-44422-2-22-22-22000000000000000000−4i4i0000000000002i−2i000000000000000000
χ634-44-4-44-24-44-422-22-222-2-2000000004-40000000000000000-22000000000000000000000000
χ644-44-4-44-24-44-422-22-222-2-200000000-4400000000000000002-2000000000000000000000000
χ654-44-4-44-2-44-4422-22-2-2-222000000000000000000004i−4i000000000000−2i2i0000000000000000
χ664-44-4-44-2-44-4422-22-2-2-22200000000000000000000−4i4i0000000000002i−2i0000000000000000
χ6788-8-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000-44400000000000000000000000000000026−2600000000000000000000000000
χ6988-8-800-40000-444000000000000000000000000000000−262600000000000000000000000000
χ708-8-880080000-88-80000000000000000000000000000000000000000000000000000000000
χ718-8-8800-400004-44000000000000000000000000000026−260000000000000000000000000000
χ728-8-8800-400004-440000000000000000000000000000−26260000000000000000000000000000

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