Finite Group Databasebeta

← Group #10849689

Character table — Group #10849689

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size1111222222222244444466888888888888888812121212121212161616161616161616161616162424242424242424242448
order12222234444666661212121244222444448888121212124444444466612121212122424242424444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11
χ4111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111111-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1
χ51111111111111111111111-1-111-1-11111-1-11111111-1-1-1-1-1-1-11-11-1-1-111-1-111-1-11111-1-1-1
χ61111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1111-1-1-1-11-1-11-11-111-1-11111-1-1-1-1-1-1111
χ71111111111111111111111-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-11-11-1-1-1-111-1-11111-1-111-1
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1111-1-1-1-11-1-1-11-111111-1-1-1-111-1-111-1-11
χ911111111111111111111-1-11111111111111111-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111
χ1111111111111111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-11111-1-11111-1
χ1211111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-11
χ1311111111111111111111-1-1-1-111-1-11111-1-11111-1-1-11111-1-1-11-11-1-1-111-1-1-1-111-1-1-1-1111
χ1411111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-11-11-111-1-111-1-1111111-1-1-1
χ1511111111111111111111-1-1-1-1-1-11111-1-1111111-1-1-11111-1-1-1-11-11-1-1-1-11111-1-1-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-111111-1-1-11-111111-1-111-1-111-1-111-1
χ172222222-2-2-2-222222-2-2-2-2222-200000000000000-2-2222-2-202-2000000000000000000000
χ182222222-2-2-2-222222-2-2-2-222-2200000000000000-2-22-2-2220-22000000000000000000000
χ192222222-2-2-2-222222-2-2-2-2-2-22-20000000000000022-2-2-22202-2000000000000000000000
χ202222222-2-2-2-222222-2-2-2-2-2-2-220000000000000022-222-2-20-22000000000000000000000
χ21222222-12222-1-1-1-1-1-1-1-1-100222222222222-1-1-1-100000002-1-1-1-1-1-1-1-1-1-1-1-100000000000
χ22222222-12222-1-1-1-1-1-1-1-1-100222222-2-2-2-2-2-211110000000-2-1-1-1-1-1-111111100000000000
χ23222222-12222-1-1-1-1-1-1-1-1-10022-2-2-2-222-2-2-2-2-1-1-1-100000002-1-11111-1-1111100000000000
χ24222222-12222-1-1-1-1-1-1-1-1-10022-2-2-2-2-2-2222211110000000-2-1-1111111-1-1-1-100000000000
χ25222222-12222-1-1-1-1-1-1-1-1-100-2-222-2-22222-2-2-1-1-1-10000000-211-11-1111-1-11100000000000
χ26222222-12222-1-1-1-1-1-1-1-1-100-2-222-2-2-2-2-2-22211110000000211-11-11-1-111-1-100000000000
χ27222222-12222-1-1-1-1-1-1-1-1-100-2-2-2-22222-2-222-1-1-1-10000000-2111-11-11111-1-100000000000
χ28222222-12222-1-1-1-1-1-1-1-1-100-2-2-2-222-2-222-2-2111100000002111-11-1-1-1-1-11100000000000
χ292222-2-222-22-2222-2-22-22-22200002-200000000002-2-20000000020-2000000002-20000000
χ302222-2-222-22-2222-2-22-22-2220000-2200000000002-2-200000000-20200000000-220000000
χ312222-2-222-22-2222-2-22-22-2-2-200002-20000000000-2220000000020-200000000-220000000
χ322222-2-222-22-2222-2-22-22-2-2-20000-220000000000-22200000000-202000000002-20000000
χ332222-2-22-22-22222-2-2-22-2222002-2000000000000-22-2000000020-200000002-2000000000
χ342222-2-22-22-22222-2-2-22-222200-22000000000000-22-20000000-2020000000-22000000000
χ352222-2-22-22-22222-2-2-22-22-2-2002-20000000000002-22000000020-20000000-22000000000
χ362222-2-22-22-22222-2-2-22-22-2-200-220000000000002-220000000-20200000002-2000000000
χ3722-2-2-22222-2-2-22-2-22-2-22200000000002-20000000002i−2i2i−2i0000000002-200000000002i−2i0
χ3822-2-2-22222-2-2-22-2-22-2-22200000000002-2000000000−2i2i−2i2i0000000002-20000000000−2i2i0
χ3922-2-2-22222-2-2-22-2-22-2-2220000000000-220000000002i−2i2i−2i000000000-220000000000−2i2i0
χ4022-2-2-22222-2-2-22-2-22-2-2220000000000-22000000000−2i2i−2i2i000000000-2200000000002i−2i0
χ4122-2-2-222-2-222-22-2-2222-2-20000000000002i−2i00000002i−2i−2i2i000000000002i−2i0000002-2000
χ4222-2-2-222-2-222-22-2-2222-2-20000000000002i−2i0000000−2i2i2i−2i000000000002i−2i000000-22000
χ4322-2-2-222-2-222-22-2-2222-2-2000000000000−2i2i00000002i−2i−2i2i00000000000−2i2i000000-22000
χ4422-2-2-222-2-222-22-2-2222-2-2000000000000−2i2i0000000−2i2i2i−2i00000000000−2i2i0000002-2000
χ45444444-2-4-4-4-4-2-2-2-2-22222004-40000000000000000000000-22000000000000000000000
χ46444444-2-4-4-4-4-2-2-2-2-2222200-4400000000000000000000002-2000000000000000000000
χ474444-4-4-24-44-4-2-2-222-22-220000004-4000000000000000000000-20200000000000000000
χ484444-4-4-24-44-4-2-2-222-22-22000000-4400000000000000000000020-200000000000000000
χ494444-4-4-2-44-44-2-2-2222-22-200004-40000000000000000000000-202000000000000000000
χ504444-4-4-2-44-44-2-2-2222-22-20000-44000000000000000000000020-2000000000000000000
χ5144-4-44-444-4-44-44-44-4-444-40000000000000000000000000000000000000000000000000
χ5244-4-44-44-444-4-44-44-44-4-440000000000000000000000000000000000000000000000000
χ5344-4-44-4-24-4-442-22-222-2-220000000000000000000000000000000023−23000000000000000
χ5444-4-44-4-24-4-442-22-222-2-2200000000000000000000000000000000−2323000000000000000
χ5544-4-44-4-2-444-42-22-22-222-2000000000000002323−23−230000000000000000000000000000000
χ5644-4-44-4-2-444-42-22-22-222-200000000000000−23−2323230000000000000000000000000000000
χ5744-4-4-44-244-4-42-222-222-2-200000000004-40000000000000000000000-220000000000000
χ5844-4-4-44-244-4-42-222-222-2-20000000000-4400000000000000000000002-20000000000000
χ5944-4-4-44-2-4-4442-222-2-2-2220000000000004i−4i0000000000000000000000−2i2i00000000000
χ6044-4-4-44-2-4-4442-222-2-2-222000000000000−4i4i00000000000000000000002i−2i00000000000
χ614-4-440040000-4-440000004-40000002-200002-22-20000000000000000000000002-200000
χ624-4-440040000-4-440000004-4000000-220000-22-22000000000000000000000000-2200000
χ634-4-440040000-4-44000000-440000002-200002-22-2000000000000000000000000-2200000
χ644-4-440040000-4-44000000-44000000-220000-22-220000000000000000000000002-200000
χ658-88-800800008-8-80000000000000000000000000000000000000000000000000000000
χ668-88-800-40000-4440000000000000000000023−23−23230000000000000000000000000000000
χ678-88-800-40000-44400000000000000000000−232323−230000000000000000000000000000000
χ688-8-8800-4000044-4000000000000004-40000-22-220000000000000000000000000000000
χ698-8-8800-4000044-400000000000000-4400002-22-20000000000000000000000000000000

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