Finite Group Databasebeta

← Group #10822584

Character table — Group #10822584

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222444444888888888888888888121212122424242424241111222222222244444488888888888888888812121212242424242424
order122222222236666666664444441212121212121212121212122222444444222222222266666666664444441212121212121212121212122222444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ41111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ511111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ611111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ92222222222-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-100000000002222222222-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ102222222222-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-11111111100000000002222222222-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111111110000000000
χ112222222222-1-1-1-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-1111100000000002222222222-1-1-1-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-111110000000000
χ122222222222-1-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-100000000002222222222-1-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-10000000000
χ1322222-2-22-2-222222-2-2-22-200000000000000000000002-2000022222-2-22-2-222222-2-2-22-200000000000000000000002-20000
χ1422222-2-22-2-222222-2-2-22-20000000000000000000000-22000022222-2-22-2-222222-2-2-22-20000000000000000000000-220000
χ152222-22-2-22-22222-22-2-2-220000000000000000000000002-2002222-22-2-22-22222-22-2-2-220000000000000000000000002-200
χ162222-22-2-22-22222-22-2-2-22000000000000000000000000-22002222-22-2-22-22222-22-2-2-22000000000000000000000000-2200
χ172222-2-22-2-222222-2-222-2-22-2000022-2-20000000000000000002222-2-22-2-222222-2-222-2-22-2000022-2-2000000000000000000
χ182222-2-22-2-222222-2-222-2-2-220000-2-2220000000000000000002222-2-22-2-222222-2-222-2-2-220000-2-222000000000000000000
χ192222-2-22-2-22-1-1-1-111-1-1112-20000-1-11133−3−333−3−300000000002222-2-22-2-22-1-1-1-111-1-1112-20000-1-11133−3−333−3−30000000000
χ202222-2-22-2-22-1-1-1-111-1-1112-20000-1-111−3−333−3−33300000000002222-2-22-2-22-1-1-1-111-1-1112-20000-1-111−3−333−3−3330000000000
χ212222-2-22-2-22-1-1-1-111-1-111-22000011-1-133−3−3−3−33300000000002222-2-22-2-22-1-1-1-111-1-111-22000011-1-133−3−3−3−3330000000000
χ222222-2-22-2-22-1-1-1-111-1-111-22000011-1-1−3−33333−3−300000000002222-2-22-2-22-1-1-1-111-1-111-22000011-1-1−3−33333−3−30000000000
χ2322-2-2222-2-2-222-2-2222-2-2-200000000000000000022-2-200000022-2-2222-2-2-222-2-2222-2-2-200000000000000000022-2-2000000
χ2422-2-2222-2-2-222-2-2222-2-2-2000000000000000000-2-22200000022-2-2222-2-2-222-2-2222-2-2-2000000000000000000-2-222000000
χ2522-2-22-2-2-22222-2-22-2-22-22002i−2i0000002i−2i2i−2i0000000000000022-2-22-2-2-22222-2-22-2-22-22002i−2i0000002i−2i2i−2i00000000000000
χ2622-2-22-2-2-22222-2-22-2-22-2200−2i2i000000−2i2i−2i2i0000000000000022-2-22-2-2-22222-2-22-2-22-2200−2i2i000000−2i2i−2i2i00000000000000
χ2722-2-22-2-2-222-1-111-111-11-1002i−2i003−33−3−ii−ii−i3i3−i3i3000000000022-2-22-2-2-222-1-111-111-11-1002i−2i003−33−3−ii−ii−i3i3−i3i30000000000
χ2822-2-22-2-2-222-1-111-111-11-1002i−2i00−33−33−ii−iii3−i3i3−i3000000000022-2-22-2-2-222-1-111-111-11-1002i−2i00−33−33−ii−iii3−i3i3−i30000000000
χ2922-2-22-2-2-222-1-111-111-11-100−2i2i003−33−3i−ii−ii3−i3i3−i3000000000022-2-22-2-2-222-1-111-111-11-100−2i2i003−33−3i−ii−ii3−i3i3−i30000000000
χ3022-2-22-2-2-222-1-111-111-11-100−2i2i00−33−33i−ii−i−i3i3−i3i3000000000022-2-22-2-2-222-1-111-111-11-100−2i2i00−33−33i−ii−i−i3i3−i3i30000000000
χ3122-2-2-22-22-2222-2-2-22-222-200002i−2i000000002i−2i−2i2i000000000022-2-2-22-22-2222-2-2-22-222-200002i−2i000000002i−2i−2i2i0000000000
χ3222-2-2-22-22-2222-2-2-22-222-20000−2i2i00000000−2i2i2i−2i000000000022-2-2-22-22-2222-2-2-22-222-20000−2i2i00000000−2i2i2i−2i0000000000
χ3322-2-2-22-22-22-1-1111-11-1-1100002i−2i3−3−33i3−i3−i3i3−iii−i000000000022-2-2-22-22-22-1-1111-11-1-1100002i−2i3−3−33i3−i3−i3i3−iii−i0000000000
χ3422-2-2-22-22-22-1-1111-11-1-1100002i−2i−333−3−i3i3i3−i3−iii−i000000000022-2-2-22-22-22-1-1111-11-1-1100002i−2i−333−3−i3i3i3−i3−iii−i0000000000
χ3522-2-2-22-22-22-1-1111-11-1-110000−2i2i3−3−33−i3i3i3−i3i−i−ii000000000022-2-2-22-22-22-1-1111-11-1-110000−2i2i3−3−33−i3i3i3−i3i−i−ii0000000000
χ3622-2-2-22-22-22-1-1111-11-1-110000−2i2i−333−3i3−i3−i3i3i−i−ii000000000022-2-2-22-22-22-1-1111-11-1-110000−2i2i−333−3i3−i3−i3i3i−i−ii0000000000
χ3722-2-2-2-2222-222-2-2-2-22-222000000000000000000000000002i−2i22-2-2-2-2222-222-2-2-2-22-222000000000000000000000000002i−2i
χ3822-2-2-2-2222-222-2-2-2-22-22200000000000000000000000000−2i2i22-2-2-2-2222-222-2-2-2-22-22200000000000000000000000000−2i2i
χ3944444-4-44-4-4-2-2-2-2-2222-22000000000000000000000000000044444-4-44-4-4-2-2-2-2-2222-220000000000000000000000000000
χ404444-44-4-44-4-2-2-2-22-2222-200000000000000000000000000004444-44-4-44-4-2-2-2-22-2222-20000000000000000000000000000
χ4144-4-4444-4-4-4-2-222-2-2-2222000000000000000000000000000044-4-4444-4-4-4-2-222-2-2-22220000000000000000000000000000
χ4244-4-4-4-4444-4-2-22222-22-2-2000000000000000000000000000044-4-4-4-4444-4-2-22222-22-2-20000000000000000000000000000
χ434-44-40000004-44-40000000000000000000000002-22-20000004-44-40000004-44-40000000000000000000000002-22-2000000
χ444-44-40000004-44-4000000000000000000000000-22-220000004-44-40000004-44-4000000000000000000000000-22-22000000
χ454-4-440000004-4-440000000000000000000000002-2-220000004-4-440000004-4-440000000000000000000000002-2-22000000
χ464-4-440000004-4-44000000000000000000000000-222-20000004-4-440000004-4-44000000000000000000000000-222-2000000
χ478-88-8000000-44-4400000000000000000000000000000000008-88-8000000-44-440000000000000000000000000000000000
χ488-8-88000000-444-400000000000000000000000000000000008-8-88000000-444-40000000000000000000000000000000000
χ49111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5011111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ511111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1
χ521111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111
χ5311111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-11111
χ5411111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111111111-1-1-1-1
χ5511111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-111
χ5611111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-111-1-1
χ572222222222-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-2-2-2-2-2-2-2-2-21111111111-2-2-2-2-2-21111111111110000000000
χ582222222222-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111111110000000000-2-2-2-2-2-2-2-2-2-21111111111-2-222221111-1-1-1-1-1-1-1-10000000000
χ592222222222-1-1-1-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-111110000000000-2-2-2-2-2-2-2-2-2-2111111111122-2-222-1-1-1-11111-1-1-1-10000000000
χ602222222222-1-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-10000000000-2-2-2-2-2-2-2-2-2-211111111112222-2-2-1-1-1-1-1-1-1-111110000000000
χ6122222-2-22-2-222222-2-2-22-200000000000000000000002-20000-2-2-2-2-222-222-2-2-2-2-2222-220000000000000000000000-220000
χ6222222-2-22-2-222222-2-2-22-20000000000000000000000-220000-2-2-2-2-222-222-2-2-2-2-2222-2200000000000000000000002-20000
χ632222-22-2-22-22222-22-2-2-220000000000000000000000002-200-2-2-2-22-222-22-2-2-2-22-2222-2000000000000000000000000-2200
χ642222-22-2-22-22222-22-2-2-22000000000000000000000000-2200-2-2-2-22-222-22-2-2-2-22-2222-20000000000000000000000002-200
χ652222-2-22-2-222222-2-222-2-22-2000022-2-2000000000000000000-2-2-2-222-222-2-2-2-2-222-2-222-220000-2-222000000000000000000
χ662222-2-22-2-222222-2-222-2-2-220000-2-222000000000000000000-2-2-2-222-222-2-2-2-2-222-2-2222-2000022-2-2000000000000000000
χ672222-2-22-2-22-1-1-1-111-1-1112-20000-1-11133−3−333−3−30000000000-2-2-2-222-222-21111-1-111-1-1-22000011-1-1−3−333−3−3330000000000
χ682222-2-22-2-22-1-1-1-111-1-1112-20000-1-111−3−333−3−3330000000000-2-2-2-222-222-21111-1-111-1-1-22000011-1-133−3−333−3−30000000000
χ692222-2-22-2-22-1-1-1-111-1-111-22000011-1-133−3−3−3−3330000000000-2-2-2-222-222-21111-1-111-1-12-20000-1-111−3−33333−3−30000000000
χ702222-2-22-2-22-1-1-1-111-1-111-22000011-1-1−3−33333−3−30000000000-2-2-2-222-222-21111-1-111-1-12-20000-1-11133−3−3−3−3330000000000
χ7122-2-2222-2-2-222-2-2222-2-2-200000000000000000022-2-2000000-2-222-2-2-2222-2-222-2-2-2222000000000000000000-2-222000000
χ7222-2-2222-2-2-222-2-2222-2-2-2000000000000000000-2-222000000-2-222-2-2-2222-2-222-2-2-222200000000000000000022-2-2000000
χ7322-2-22-2-2-22222-2-22-2-22-22002i−2i0000002i−2i2i−2i00000000000000-2-222-2222-2-2-2-222-222-22-200−2i2i000000−2i2i−2i2i00000000000000
χ7422-2-22-2-2-22222-2-22-2-22-2200−2i2i000000−2i2i−2i2i00000000000000-2-222-2222-2-2-2-222-222-22-2002i−2i0000002i−2i2i−2i00000000000000
χ7522-2-22-2-2-222-1-111-111-11-1002i−2i003−33−3−ii−ii−i3i3−i3i30000000000-2-222-2222-2-211-1-11-1-11-1100−2i2i00−33−33i−ii−ii3−i3i3−i30000000000
χ7622-2-22-2-2-222-1-111-111-11-1002i−2i00−33−33−ii−iii3−i3i3−i30000000000-2-222-2222-2-211-1-11-1-11-1100−2i2i003−33−3i−ii−i−i3i3−i3i30000000000
χ7722-2-22-2-2-222-1-111-111-11-100−2i2i003−33−3i−ii−ii3−i3i3−i30000000000-2-222-2222-2-211-1-11-1-11-11002i−2i00−33−33−ii−ii−i3i3−i3i30000000000
χ7822-2-22-2-2-222-1-111-111-11-100−2i2i00−33−33i−ii−i−i3i3−i3i30000000000-2-222-2222-2-211-1-11-1-11-11002i−2i003−33−3−ii−iii3−i3i3−i30000000000
χ7922-2-2-22-22-2222-2-2-22-222-200002i−2i000000002i−2i−2i2i0000000000-2-2222-22-22-2-2-2222-22-2-220000−2i2i00000000−2i2i2i−2i0000000000
χ8022-2-2-22-22-2222-2-2-22-222-20000−2i2i00000000−2i2i2i−2i0000000000-2-2222-22-22-2-2-2222-22-2-2200002i−2i000000002i−2i−2i2i0000000000
χ8122-2-2-22-22-22-1-1111-11-1-1100002i−2i3−3−33i3−i3−i3i3−iii−i0000000000-2-2222-22-22-211-1-1-11-111-10000−2i2i−333−3−i3i3i3−i3i−i−ii0000000000
χ8222-2-2-22-22-22-1-1111-11-1-1100002i−2i−333−3−i3i3i3−i3−iii−i0000000000-2-2222-22-22-211-1-1-11-111-10000−2i2i3−3−33i3−i3−i3i3i−i−ii0000000000
χ8322-2-2-22-22-22-1-1111-11-1-110000−2i2i3−3−33−i3i3i3−i3i−i−ii0000000000-2-2222-22-22-211-1-1-11-111-100002i−2i−333−3i3−i3−i3i3−iii−i0000000000
χ8422-2-2-22-22-22-1-1111-11-1-110000−2i2i−333−3i3−i3−i3i3i−i−ii0000000000-2-2222-22-22-211-1-1-11-111-100002i−2i3−3−33−i3i3i3−i3−iii−i0000000000
χ8522-2-2-2-2222-222-2-2-2-22-222000000000000000000000000002i−2i-2-22222-2-2-22-2-22222-22-2-200000000000000000000000000−2i2i
χ8622-2-2-2-2222-222-2-2-2-22-22200000000000000000000000000−2i2i-2-22222-2-2-22-2-22222-22-2-2000000000000000000000000002i−2i
χ8744444-4-44-4-4-2-2-2-2-2222-220000000000000000000000000000-4-4-4-4-444-44422222-2-2-22-20000000000000000000000000000
χ884444-44-4-44-4-2-2-2-22-2222-20000000000000000000000000000-4-4-4-44-444-442222-22-2-2-220000000000000000000000000000
χ8944-4-4444-4-4-4-2-222-2-2-22220000000000000000000000000000-4-444-4-4-444422-2-2222-2-2-20000000000000000000000000000
χ9044-4-4-4-4444-4-2-22222-22-2-20000000000000000000000000000-4-44444-4-4-4422-2-2-2-22-2220000000000000000000000000000
χ914-44-40000004-44-40000000000000000000000002-22-2000000-44-44000000-44-44000000000000000000000000-22-22000000
χ924-44-40000004-44-4000000000000000000000000-22-22000000-44-44000000-44-440000000000000000000000002-22-2000000
χ934-4-440000004-4-440000000000000000000000002-2-22000000-444-4000000-444-4000000000000000000000000-222-2000000
χ944-4-440000004-4-44000000000000000000000000-222-2000000-444-4000000-444-40000000000000000000000002-2-22000000
χ958-88-8000000-44-440000000000000000000000000000000000-88-880000004-44-40000000000000000000000000000000000
χ968-8-88000000-444-40000000000000000000000000000000000-888-80000004-4-440000000000000000000000000000000000

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