Finite Group Databasebeta

← Group #10826744

Character table — Group #10826744

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1122222222222444444444444444444448888888888816161616161616161616161624242424242424242424242424242424
order122222222366622224444446666661212121246666121212121212444412121212121212122222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ5111111111111111-1-111-1-1-1-1111111-1-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-1111-1111-1-1-1-1-111-1-1
χ6111111111111111-1-111-1-1-1-1111111-1-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-11-1-1-111111-1-111
χ7111111111111111-1-111-1-1-1-1111111-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1111111-1111-11-1-1-1-1-1-111
χ8111111111111111-1-111-1-1-1-1111111-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-11111-1-11-1-1-11-1111111-1-1
χ91111111111111-1-111-1-111-1-1111111-1-1-1-1-1-1-111-1-111-1-11-11-111-1-111-1-11-1111-11111-1-1-1-1-1-1
χ101111111111111-1-111-1-111-1-1111111-1-1-1-1-1-1-111-1-111-1-11-11-111-1-111-1-1-11-1-1-11-1-1-1-1111111
χ111111111111111-1-111-1-111-1-1111111-1-1-1-1-1-1-111-1-111-1-1-11-11-1-111-1-1111-1-1-11-1-1-111-1-11111
χ121111111111111-1-111-1-111-1-1111111-1-1-1-1-1-1-111-1-111-1-1-11-11-1-111-1-111-1111-1111-1-111-1-1-1-1
χ131111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1111-11-11-11-1-1-111-1-111
χ141111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-111-11-11-11-1111-1-111-1-1
χ151111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-111-1-1-11111-1-11-1-111-1-11-1-11111-1-1
χ161111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-111-1-1-11111-1-1-111-1-111-111-1-1-1-111
χ17222222222-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ18222222222-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ19222222222-1-1-1-122-2-222-2-2-2-2-1-1-1-1-1-11111-2-1-111-1-1111122-2-2-1-1-1-111110000000000000000
χ20222222222-1-1-1-122-2-222-2-2-2-2-1-1-1-1-1-11111-2-1-111-1-11111-2-2221111-1-1-1-10000000000000000
χ21222222222-1-1-1-1-2-222-2-222-2-2-1-1-1-1-1-11111-211-1-111-1-1112-22-2-1-111-1-1110000000000000000
χ22222222222-1-1-1-1-2-222-2-222-2-2-1-1-1-1-1-11111-211-1-111-1-111-22-2211-1-111-1-10000000000000000
χ23222222222-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1211111111-1-12-2-22-1-11111-1-10000000000000000
χ24222222222-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1211111111-1-1-222-211-1-1-1-1110000000000000000
χ25222-2-2-2-22222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-222222-2-2-2-2220000000000000000000000000000
χ26222-2-2-2-222222222-2-2-2-2222222-2-2-2-22222-222-2-2-2-222-2-20000000000000000000000000000
χ27222-2-2-2-2222222-2-22222-2-22222-2-2-2-22222-2-2-22222-2-2-2-20000000000000000000000000000
χ28222-2-2-2-2222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-22-2-2-2-22222220000000000000000000000000000
χ29222-2-2-2-222-1-1-1-12222-2-2-2-2-2-2-1-1111111112-1-1-1-11111-1-100003−33−33−33−30000000000000000
χ30222-2-2-2-222-1-1-1-12222-2-2-2-2-2-2-1-1111111112-1-1-1-11111-1-10000−33−33−33−330000000000000000
χ31222-2-2-2-222-1-1-1-122-2-2-2-22222-1-11111-1-1-1-1-2-1-11111-1-11100003−33−3−33−330000000000000000
χ32222-2-2-2-222-1-1-1-122-2-2-2-22222-1-11111-1-1-1-1-2-1-11111-1-1110000−33−333−33−30000000000000000
χ33222-2-2-2-222-1-1-1-1-2-22222-2-222-1-11111-1-1-1-1-211-1-1-1-1111100003−3−333−3−330000000000000000
χ34222-2-2-2-222-1-1-1-1-2-22222-2-222-1-11111-1-1-1-1-211-1-1-1-111110000−333−3−333−30000000000000000
χ35222-2-2-2-222-1-1-1-1-2-2-2-22222-2-2-1-11111111121111-1-1-1-1-1-100003−3−33−333−30000000000000000
χ36222-2-2-2-222-1-1-1-1-2-2-2-22222-2-2-1-11111111121111-1-1-1-1-1-10000−333−33−3−330000000000000000
χ3722-222-2-22-22-2-22002-2002-2002-222-2-200000002-2002-2000000000000002000-20002-2000000
χ3822-222-2-22-22-2-22002-2002-2002-222-2-200000002-2002-200000000000000-20002000-22000000
χ3922-222-2-22-22-2-2200-2200-22002-222-2-20000000-2200-22000000000000002000-2000-22000000
χ4022-222-2-22-22-2-2200-2200-22002-222-2-20000000-2200-2200000000000000-200020002-2000000
χ4122-22-22-2-222-2-222-2002-20000-222-22-2000002-2002-20000000000000000002000-2000002-200
χ4222-22-22-2-222-2-222-2002-20000-222-22-2000002-2002-2000000000000000000-2000200000-2200
χ4322-22-22-2-222-2-22-2200-220000-222-22-200000-2200-220000000000000000002000-200000-2200
χ4422-22-22-2-222-2-22-2200-220000-222-22-200000-2200-22000000000000000000-20002000002-200
χ4522-2-22-22-222-2-222-200-220000-22-22-22000002-200-2200000000000000000002000-20000002-2
χ4622-2-22-22-222-2-222-200-220000-22-22-22000002-200-220000000000000000000-20002000000-22
χ4722-2-22-22-222-2-22-22002-20000-22-22-2200000-22002-200000000000000000002000-2000000-22
χ4822-2-22-22-222-2-22-22002-20000-22-22-2200000-22002-20000000000000000000-200020000002-2
χ4922-2-2-2222-22-2-22002-200-22002-2-2-22200000002-200-220000000000000002000-200002-20000
χ5022-2-2-2222-22-2-22002-200-22002-2-2-22200000002-200-22000000000000000-200020000-220000
χ5122-2-2-2222-22-2-2200-22002-2002-2-2-2220000000-22002-20000000000000002000-20000-220000
χ5222-2-2-2222-22-2-2200-22002-2002-2-2-2220000000-22002-2000000000000000-2000200002-20000
χ534444-4-44-4-444440000000000-4-44-4-440000000000000000000000000000000000000000000
χ544444-4-44-4-4-2-2-2-2000000000022-222-2−2i3−2i32i32i3000000000−2i32i30000000000000000000000000000
χ554444-4-44-4-4-2-2-2-2000000000022-222-22i32i3−2i3−2i30000000002i3−2i30000000000000000000000000000
χ56444-444-4-4-444440000000000-4-4-444-40000000000000000000000000000000000000000000
χ57444-444-4-4-4-2-2-2-20000000000222-2-22−2i3−2i32i32i30000000002i3−2i30000000000000000000000000000
χ58444-444-4-4-4-2-2-2-20000000000222-2-222i32i3−2i3−2i3000000000−2i32i30000000000000000000000000000
χ5944-444-4-44-4-222-2004-4004-400-22-2-2220000000-2200-22000000000000000000000000000000
χ6044-444-4-44-4-222-200-4400-4400-22-2-22200000002-2002-2000000000000000000000000000000
χ6144-44-44-4-44-222-24-4004-400002-2-22-2200000-2200-2200000000000000000000000000000000
χ6244-44-44-4-44-222-2-4400-4400002-2-22-22000002-2002-200000000000000000000000000000000
χ6344-4-44-44-44-222-24-400-4400002-22-22-200000-22002-200000000000000000000000000000000
χ6444-4-44-44-44-222-2-44004-400002-22-22-2000002-200-2200000000000000000000000000000000
χ6544-4-4-4444-4-222-2004-400-4400-2222-2-20000000-22002-2000000000000000000000000000000
χ6644-4-4-4444-4-222-200-44004-400-2222-2-200000002-200-22000000000000000000000000000000
χ678-80000000800-8000000004i−4i0000004i−4i4i−4i000000000000000000000000000000000000000
χ688-80000000800-800000000−4i4i000000−4i4i−4i4i000000000000000000000000000000000000000
χ698-80000000-4−4i34i34000000004i−4i0000004ζ7−4ζ74ζ11−4ζ11000000000000000000000000000000000000000
χ708-80000000-4−4i34i3400000000−4i4i000000−4ζ74ζ7−4ζ114ζ11000000000000000000000000000000000000000
χ718-80000000-44i3−4i34000000004i−4i0000004ζ11−4ζ114ζ7−4ζ7000000000000000000000000000000000000000
χ728-80000000-44i3−4i3400000000−4i4i000000−4ζ114ζ11−4ζ74ζ7000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.