Finite Group Databasebeta

← Group #13149810

Character table — Group #13149810

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11222222222226666991212121212121212121212121212181818181818181818181836363636727272721122222222222666699121212121212121212121212121218181818181818181818183636363672727272
order123468812122424242433662236121212122424242424242424466881212242424242244661212226468812122424242466662266121212122424242424242424466881212242424242244661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11-11-11-11-111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1
χ411111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11
χ511111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-111-1-111-1-111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-111-1-111-1-1
χ611111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-111-1-11111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-111-1-111
χ711111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-111-1-1111111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-111-1-11
χ811111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-1-111-111111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-1-111-1
χ922222222222222-12-100-1-12-1-1-122-1-1-1-1-1-10000000000002020-10-122222222222222-12-100-1-12-1-1-122-1-1-1-1-1-10000000000002020-10-1
χ1022222222222222-12-100-1-12-1-1-122-1-1-1-1-1-1000000000000-20-2010122222222222222-12-100-1-12-1-1-122-1-1-1-1-1-1000000000000-20-20101
χ112222222222222-12-1200-1-1-12-1-1-1-122-1-1-1-1000000000002020-10-102222222222222-12-1200-1-1-12-1-1-1-122-1-1-1-1000000000002020-10-10
χ122222222222222-12-1200-1-1-12-1-1-1-122-1-1-1-100000000000-20-2010102222222222222-12-1200-1-1-12-1-1-1-122-1-1-1-100000000000-20-201010
χ1322222-2-222-2-2-2-22-12-100-1-12-1-1-1-2-211111100000000000020-20-10122222-2-222-2-2-2-22-12-100-1-12-1-1-1-2-211111100000000000020-20-101
χ1422222-2-222-2-2-2-22-12-100-1-12-1-1-1-2-2111111000000000000-202010-122222-2-222-2-2-2-22-12-100-1-12-1-1-1-2-2111111000000000000-202010-1
χ1522222-2-222-2-2-2-2-12-1200-1-1-12-1-111-2-211110000000000020-20-101022222-2-222-2-2-2-2-12-1200-1-1-12-1-111-2-211110000000000020-20-1010
χ1622222-2-222-2-2-2-2-12-1200-1-1-12-1-111-2-2111100000000000-202010-1022222-2-222-2-2-2-2-12-1200-1-1-12-1-111-2-2111100000000000-202010-10
χ17222-2200-2-2000022222222-2-2-2-200000000-22200-2-2000000000000222-2200-2-2000022222222-2-2-2-200000000-22200-2-2000000000000
χ18222-2200-2-200002222-2-222-2-2-2-2000000002-2-20022000000000000222-2200-2-200002222-2-222-2-2-2-2000000002-2-20022000000000000
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χ202-220-2−i2i200−i2−i2i2i222-2-2-222-20000−i2i2−i2i2−i2−i2i2i20-22i2−i200i2i2−i2−i2000000002-220-2−i2i200−i2−i2i2i222-2-2-222-20000−i2i2−i2i2−i2−i2i2i20-22i2−i200i2i2−i2−i200000000
χ212-220-2i2−i200i2i2−i2−i222-2-22-22-20000i2−i2i2−i2i2i2−i2−i202-2i2−i200i2i2−i2−i2000000002-220-2i2−i200i2i2−i2−i222-2-22-22-20000i2−i2i2−i2i2i2−i2−i202-2i2−i200i2i2−i2−i200000000
χ222-220-2i2−i200i2i2−i2−i222-2-2-222-20000i2−i2i2−i2i2i2−i2−i20-22−i2i200−i2−i2i2i2000000002-220-2i2−i200i2i2−i2−i222-2-2-222-20000i2−i2i2−i2i2i2−i2−i20-22−i2i200−i2−i2i2i200000000
χ234444444444444-2-2-2-20011-2-211-2-2-2-2111100000000000000000004444444444444-2-2-2-20011-2-211-2-2-2-211110000000000000000000
χ2444444-4-444-4-4-4-4-2-2-2-20011-2-2112222-1-1-1-1000000000000000000044444-4-444-4-4-4-4-2-2-2-20011-2-2112222-1-1-1-10000000000000000000
χ25444-4400-4-400004-24-200-2-2-4222000000000000000000000000000444-4400-4-400004-24-200-2-2-4222000000000000000000000000000
χ26444-4400-4-40000-24-2400-2-22-422000000000000000000000000000444-4400-4-40000-24-2400-2-22-422000000000000000000000000000
χ27444-4400-4-40000-2-2-2-2001122-1-100003i−3i3i−3i0000000000000000000444-4400-4-40000-2-2-2-2001122-1-100003i−3i3i−3i0000000000000000000
χ28444-4400-4-40000-2-2-2-2001122-1-10000−3i3i−3i3i0000000000000000000444-4400-4-40000-2-2-2-2001122-1-10000−3i3i−3i3i0000000000000000000
χ294-440-4−2i22i200−2i2−2i22i22i24-2-4200-220000−2i22i2i2−i2i2i2−i2−i200000000000000000004-440-4−2i22i200−2i2−2i22i22i24-2-4200-220000−2i22i2i2−i2i2i2−i2−i20000000000000000000
χ304-440-4−2i22i200−2i2−2i22i22i2-242-400-220000i2−i2−2i22i2i2i2−i2−i200000000000000000004-440-4−2i22i200−2i2−2i22i22i2-242-400-220000i2−i2−2i22i2i2i2−i2−i20000000000000000000
χ314-440-4−2i22i200−2i2−2i22i22i2-2-222001-1003i−3ii2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ2300000000000000000004-440-4−2i22i200−2i2−2i22i22i2-2-222001-1003i−3ii2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ230000000000000000000
χ324-440-4−2i22i200−2i2−2i22i22i2-2-222001-100−3i3ii2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ2300000000000000000004-440-4−2i22i200−2i2−2i22i22i2-2-222001-100−3i3ii2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ230000000000000000000
χ334-440-42i2−2i2002i22i2−2i2−2i24-2-4200-2200002i2−2i2−i2i2−i2−i2i2i200000000000000000004-440-42i2−2i2002i22i2−2i2−2i24-2-4200-2200002i2−2i2−i2i2−i2−i2i2i20000000000000000000
χ344-440-42i2−2i2002i22i2−2i2−2i2-242-400-220000−i2i22i2−2i2−i2−i2i2i200000000000000000004-440-42i2−2i2002i22i2−2i2−2i2-242-400-220000−i2i22i2−2i2−i2−i2i2i20000000000000000000
χ354-440-42i2−2i2002i22i2−2i2−2i2-2-222001-1003i−3i−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ2300000000000000000004-440-42i2−2i2002i22i2−2i2−2i2-2-222001-1003i−3i−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ230000000000000000000
χ364-440-42i2−2i2002i22i2−2i2−2i2-2-222001-100−3i3i−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ2300000000000000000004-440-42i2−2i2002i22i2−2i2−2i2-2-222001-100−3i3i−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ230000000000000000000
χ3766-36-366-3-3-3-3-3-3000022000000000000002-1-122-1-1-1-1-1-10000000066-36-366-3-3-3-3-3-3000022000000000000002-1-122-1-1-1-1-1-100000000
χ3866-36-366-3-3-3-3-3-30000-2-200000000000000-211-2-21111110000000066-36-366-3-3-3-3-3-30000-2-200000000000000-211-2-211111100000000
χ3966-36-3-6-6-3-33333000022000000000000002-1-1-2-2-1-111110000000066-36-3-6-6-3-33333000022000000000000002-1-1-2-2-1-1111100000000
χ4066-36-3-6-6-3-333330000-2-200000000000000-2112211-1-1-1-10000000066-36-3-6-6-3-333330000-2-200000000000000-2112211-1-1-1-100000000
χ4166-3-6-3003333−3333−3300002200000000000000-2-1-100113−33−30000000066-3-6-3003333−3333−3300002200000000000000-2-1-100113−33−300000000
χ4266-3-6-3003333−3333−330000-2-20000000000000021100-1-1−33−330000000066-3-6-3003333−3333−330000-2-20000000000000021100-1-1−33−3300000000
χ4366-3-6-30033−3333−333300002200000000000000-2-1-10011−33−330000000066-3-6-30033−3333−333300002200000000000000-2-1-10011−33−3300000000
χ4466-3-6-30033−3333−33330000-2-20000000000000021100-1-13−33−30000000066-3-6-30033−3333−33330000-2-20000000000000021100-1-13−33−300000000
χ456-6-303−3i23i233−333ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ2300002-2000000000000000-11−i2i23−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000006-6-303−3i23i233−333ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ2300002-2000000000000000-11−i2i23−3ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ2300000000
χ466-6-303−3i23i233−333ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ230000-220000000000000001-1i2−i2−33−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000006-6-303−3i23i233−333ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ230000-220000000000000001-1i2−i2−33−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2300000000
χ476-6-303−3i23i2−33333ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ700002-2000000000000000-11−i2i2−33ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000006-6-303−3i23i2−33333ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ700002-2000000000000000-11−i2i2−33ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ700000000
χ486-6-303−3i23i2−33333ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ70000-220000000000000001-1i2−i23−3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000006-6-303−3i23i2−33333ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ70000-220000000000000001-1i2−i23−3−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ700000000
χ496-6-3033i2−3i233−33−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ2300002-2000000000000000-11i2−i23−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000006-6-3033i2−3i233−33−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ2300002-2000000000000000-11i2−i23−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2300000000
χ506-6-3033i2−3i233−33−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ230000-220000000000000001-1−i2i2−33ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000006-6-3033i2−3i233−33−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ230000-220000000000000001-1−i2i2−33ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ2300000000
χ516-6-3033i2−3i2−3333−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ700002-2000000000000000-11i2−i2−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000006-6-3033i2−3i2−3333−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ700002-2000000000000000-11i2−i2−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ700000000
χ526-6-3033i2−3i2−3333−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ70000-220000000000000001-1−i2i23−3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000006-6-3033i2−3i2−3333−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ70000-220000000000000001-1−i2i23−3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ700000000
χ531111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5511111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-11-11-11
χ5611111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-11-11-1
χ5711111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-11111-1-111-1-111
χ5811111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1111111-1-111-1-1
χ5911111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-111-1-11-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-111111111111-1-111-1-1-1-1-111-1-111-1
χ6011111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-111111111111-1-111-1-1-1-11-1-111-1-11
χ6122222222222222-12-100-1-12-1-1-122-1-1-1-1-1-10000000000002020-10-1-2-2-2-2-2-2-2-2-2-2-2-2-2-21-210011-2111-2-2111111000000000000-20-20101
χ6222222222222222-12-100-1-12-1-1-122-1-1-1-1-1-1000000000000-20-20101-2-2-2-2-2-2-2-2-2-2-2-2-2-21-210011-2111-2-21111110000000000002020-10-1
χ632222222222222-12-1200-1-1-12-1-1-1-122-1-1-1-1000000000002020-10-10-2-2-2-2-2-2-2-2-2-2-2-2-21-21-200111-21111-2-2111100000000000-20-201010
χ642222222222222-12-1200-1-1-12-1-1-1-122-1-1-1-100000000000-20-201010-2-2-2-2-2-2-2-2-2-2-2-2-21-21-200111-21111-2-21111000000000002020-10-10
χ6522222-2-222-2-2-2-22-12-100-1-12-1-1-1-2-211111100000000000020-20-101-2-2-2-2-222-2-22222-21-210011-211122-1-1-1-1-1-1000000000000-202010-1
χ6622222-2-222-2-2-2-22-12-100-1-12-1-1-1-2-2111111000000000000-202010-1-2-2-2-2-222-2-22222-21-210011-211122-1-1-1-1-1-100000000000020-20-101
χ6722222-2-222-2-2-2-2-12-1200-1-1-12-1-111-2-211110000000000020-20-1010-2-2-2-2-222-2-222221-21-200111-211-1-122-1-1-1-100000000000-202010-10
χ6822222-2-222-2-2-2-2-12-1200-1-1-12-1-111-2-2111100000000000-202010-10-2-2-2-2-222-2-222221-21-200111-211-1-122-1-1-1-10000000000020-20-1010
χ69222-2200-2-2000022222222-2-2-2-200000000-22200-2-2000000000000-2-2-22-200220000-2-2-2-2-2-2-2-22222000000002-2-20022000000000000
χ70222-2200-2-200002222-2-222-2-2-2-2000000002-2-20022000000000000-2-2-22-200220000-2-2-2-222-2-2222200000000-22200-2-2000000000000
χ712-220-2−i2i200−i2−i2i2i222-2-22-22-20000−i2i2−i2i2−i2−i2i2i202-2−i2i200−i2−i2i2i200000000-22-202i2−i200i2i2−i2−i2-2-222-22-220000i2−i2i2−i2i2i2−i2−i20-22i2−i200i2i2−i2−i200000000
χ722-220-2−i2i200−i2−i2i2i222-2-2-222-20000−i2i2−i2i2−i2−i2i2i20-22i2−i200i2i2−i2−i200000000-22-202i2−i200i2i2−i2−i2-2-2222-2-220000i2−i2i2−i2i2i2−i2−i202-2−i2i200−i2−i2i2i200000000
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χ1016-6-3033i2−3i233−33−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ2300002-2000000000000000-11i2−i23−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2300000000-6630-3−3i23i2−33333ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ230000-220000000000000001-1−i2i2−33ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ2300000000
χ1026-6-3033i2−3i233−33−3ζ5−3ζ7−3ζ13−3ζ233ζ5+3ζ73ζ13+3ζ230000-220000000000000001-1−i2i2−33ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ2300000000-6630-3−3i23i2−33333ζ5+3ζ73ζ13+3ζ23−3ζ5−3ζ7−3ζ13−3ζ2300002-2000000000000000-11i2−i23−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2300000000
χ1036-6-3033i2−3i2−3333−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ700002-2000000000000000-11i2−i2−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ700000000-6630-3−3i23i233−333ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ70000-220000000000000001-1−i2i23−3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ700000000
χ1046-6-3033i2−3i2−3333−3ζ13−3ζ23−3ζ5−3ζ73ζ13+3ζ233ζ5+3ζ70000-220000000000000001-1−i2i23−3ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ700000000-6630-3−3i23i233−333ζ13+3ζ233ζ5+3ζ7−3ζ13−3ζ23−3ζ5−3ζ700002-2000000000000000-11i2−i2−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ700000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.