Finite Group Databasebeta

← Group #13155938

Character table — Group #13155938

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size11222222222222244444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212242424242424242424242424363636363636727272727272216
order12233344666661212333666666666121212121212121212121236666121212121212122224446666661212121212121212121212121212121212126666666661212122466121248121224248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1111111-1-11111-1-1111111111111-111-1-11111-1-1-1-1-1-1-1-1-11-111-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1111
χ511111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111111111111-1-111-1-1-1-1111-1-1-1-1-1-1-11-1-111-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1111-1-1-1-1-1-11-111-1-11
χ711111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ9222222-2-222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-22-2000022-2-20000000000000000000002-20022-2-20000000000000000
χ10222222-2-222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-220000-2-222000000000000000000000-2200-2-2220000000000000000
χ1122222-122222-12222-1-1-1-1-12-1222-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200-1-1-1-1-1-10000-1-1000000000000222-1-1-1-1-1-12-1-122-1-1-1-10000000
χ1222222-122222-12222-1-1-1-1-12-1222-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-200-1-1-1-111000011000000000000-22211-1-1-1-1-211-2-211110000000
χ1322222-122222-12222-1-1-1-1-12-1222-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222001111-1-10000-1-10000000000002-2-2-1-111112-1-1-2-211110000000
χ1422222-122222-12222-1-1-1-1-12-1222-12-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200111111000011000000000000-2-2-2111111-21122-1-1-1-10000000
χ1522222-1-2-2222-12-2-22-1-1-1-1-12-1222-1-211-2-2-2-2-2-211-1-1-1-1-111111112-20000-1-111−i3i30000−i3i300000000000002-2−i3i3-1-1110−i3i300−i3i3−i3i30000000
χ1622222-1-2-2222-12-2-22-1-1-1-1-12-1222-1-211-2-2-2-2-2-211-1-1-1-1-111111112-20000-1-111i3−i30000i3−i300000000000002-2i3−i3-1-1110i3−i300i3−i3i3−i30000000
χ1722222-1-2-2222-12-2-22-1-1-1-1-12-1222-1-211-2-2-2-2-2-211-1-1-1-1-11111111-22000011-1-1−i3i30000−i3i30000000000000-22−i3i311-1-10−i3i300i3−i3i3−i30000000
χ1822222-1-2-2222-12-2-22-1-1-1-1-12-1222-1-211-2-2-2-2-2-211-1-1-1-1-11111111-22000011-1-1i3−i30000i3−i30000000000000-22i3−i311-1-10i3−i300−i3i3−i3i30000000
χ192222-1222-1-122-122-12-12-1-1-1-12-1-12222-1-1-1-1-1-122-12-1-1-1-1-12-1-1-1-1220022222200-1-1-1-1002222-1-1-1-1-1-1-1-10-1-100-1-1-1-100000000020-1-1000
χ202222-1222-1-122-122-12-12-1-1-1-12-1-12222-1-1-1-1-1-122-12-1-1-1-1-12-1-1-1-12200-2-2222200111100-2-2-2-2111111110-1-100-1-1-1-1000000000-2011000
χ212222-1222-1-122-122-12-12-1-1-1-12-1-12222-1-1-1-1-1-122-12-1-1-1-1-12-1-1-1-1-2-20022-2-2-2-200-1-1-1-1002222-1-1-1-1-1-1-1-1011001111000000000-2011000
χ222222-1222-1-122-122-12-12-1-1-1-12-1-12222-1-1-1-1-1-122-12-1-1-1-1-12-1-1-1-1-2-200-2-2-2-2-2-200111100-2-2-2-21111111101100111100000000020-1-1000
χ232222-12-2-2-1-122-1-2-2-12-12-1-1-1-12-1-12-2-2-2111111-2-2-12-1-1-111-211112-2000022-2-200−i3−i3i3i3000000−i3−i3−i3−i3i3i3i3i30-1100-1-11100000000000−i3i3000
χ242222-12-2-2-1-122-1-2-2-12-12-1-1-1-12-1-12-2-2-2111111-2-2-12-1-1-111-211112-2000022-2-200i3i3−i3−i3000000i3i3i3i3−i3−i3−i3−i30-1100-1-11100000000000i3−i3000
χ252222-12-2-2-1-122-1-2-2-12-12-1-1-1-12-1-12-2-2-2111111-2-2-12-1-1-111-21111-220000-2-22200−i3−i3i3i3000000−i3−i3−i3−i3i3i3i3i301-10011-1-100000000000i3−i3000
χ262222-12-2-2-1-122-1-2-2-12-12-1-1-1-12-1-12-2-2-2111111-2-2-12-1-1-111-21111-220000-2-22200i3i3−i3−i3000000i3i3i3i3−i3−i3−i3−i301-10011-1-100000000000−i3i3000
χ27222-1222222-122-1-1-1-12222-12-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1002222000022222222-1-1-1-1-1-1-1-1-1-1-1-1-100-1-10000-1-1-10000000200-1-10
χ28222-1222222-122-1-1-1-12222-12-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-10022-2-2000022-2-2-2-222111111111111-100-1-10000-1-1-10000000-200110
χ29222-1222222-122-1-1-1-12222-12-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-100-2-2220000-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-11001100001110000000-200110
χ30222-1222222-122-1-1-1-12222-12-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-100-2-2-2-20000-2-2-2-2-2-2-2-21111111111111001100001110000000200-1-10
χ3122-22222-2-2-222222222-2-2-222-2-2-22-22-22-222-2-2222-2-2-222-2-222-2-20000000000000000000000000000000000000000002-222-2-20000000
χ3222-22222-2-2-222222222-2-2-222-2-2-22-22-22-222-2-2222-2-2-222-2-222-2-2000000000000000000000000000000000000000000-22-2-2220000000
χ3322-2222-22-2-2222-2-2222-2-2-222-2-2-222-22-22-2-222-2-22-2-2-22-222-2-222002-2000000220000-2-2000000000000200220000-2-2-20000000000000
χ3422-2222-22-2-2222-2-2222-2-2-222-2-2-222-22-22-2-222-2-22-2-2-22-222-2-22200-22000000-2-2000022000000000000-200-2-200002220000000000000
χ3522-222-12-2-2-22-12222-1-11112-1-2-2-2-1-2-112-222-2-2-1-1-1111-1-111-1-111000000−i3i3−i3i3−i3i30000i3−i3000000000000000−i3i3−i3i3−i3i30i3−i32-2-1-1110000000
χ3622-222-12-2-2-22-12222-1-11112-1-2-2-2-1-2-112-222-2-2-1-1-1111-1-111-1-111000000−i3i3−i3i3i3−i30000−i3i3000000000000000i3−i3−i3i3−i3i30−i3i3-2211-1-10000000
χ3722-222-12-2-2-22-12222-1-11112-1-2-2-2-1-2-112-222-2-2-1-1-1111-1-111-1-111000000i3−i3i3−i3−i3i30000i3−i3000000000000000−i3i3i3−i3i3−i30i3−i3-2211-1-10000000
χ3822-222-12-2-2-22-12222-1-11112-1-2-2-2-1-2-112-222-2-2-1-1-1111-1-111-1-111000000i3−i3i3−i3i3−i30000−i3i3000000000000000i3−i3i3−i3i3−i30−i3i32-2-1-1110000000
χ3922-222-1-22-2-22-12-2-22-1-11112-1-2-2-2-121-1-22-2-22211-1111-11-1-111-1-1002-200−i3i3i3−i3-1-1000011000000000000200-1-1−i3i3i3−i3-21100−i3i3i3−i30000000
χ4022-222-1-22-2-22-12-2-22-1-11112-1-2-2-2-121-1-22-2-22211-1111-11-1-111-1-1002-200i3−i3−i3i3-1-1000011000000000000200-1-1i3−i3−i3i3-21100i3−i3−i3i30000000
χ4122-222-1-22-2-22-12-2-22-1-11112-1-2-2-2-121-1-22-2-22211-1111-11-1-111-1-100-2200−i3i3i3−i3110000-1-1000000000000-20011−i3i3i3−i32-1-100i3−i3−i3i30000000
χ4222-222-1-22-2-22-12-2-22-1-11112-1-2-2-2-121-1-22-2-22211-1111-11-1-111-1-100-2200i3−i3−i3i3110000-1-1000000000000-20011i3−i3−i3i32-1-100−i3i3i3−i30000000
χ4322-2-122-22-2-2-12211-1-12-2-2-2-12111-1-1-22-2211-1-111-1111-1-22-111-1-1002-2000000220000-2-233−3−333−3−333−3−3-100-1-1000011100000000003−30
χ4422-2-122-22-2-2-12211-1-12-2-2-2-12111-1-1-22-2211-1-111-1111-1-22-111-1-1002-2000000220000-2-2−3−333−3−333−3−333-100-1-100001110000000000−330
χ4522-2-122-22-2-2-12211-1-12-2-2-2-12111-1-1-22-2211-1-111-1111-1-22-111-1-100-22000000-2-200002233−3−333−3−333−3−3100110000-1-1-10000000000−330
χ4622-2-122-22-2-2-12211-1-12-2-2-2-12111-1-1-22-2211-1-111-1111-1-22-111-1-100-22000000-2-2000022−3−333−3−333−3−333100110000-1-1-100000000003−30
χ474444-2-244-2-24-2-244-2-21-211-214-2-2-24-2-2-2-2-2-2-2-2-2-21-211111-21111440000-2-2-2-2000000000000000000000-2-20011110000000000000000
χ484444-2-244-2-24-2-244-2-21-211-214-2-2-24-2-2-2-2-2-2-2-2-2-21-211111-21111-4-4000022220000000000000000000002200-1-1-1-10000000000000000
χ494444-2-2-4-4-2-24-2-2-4-4-2-21-211-214-2-2-2-422222222221-2111-1-12-1-1-1-14-40000-2-222000000000000000000000-220011-1-10000000000000000
χ504444-2-2-4-4-2-24-2-2-4-4-2-21-211-214-2-2-2-422222222221-2111-1-12-1-1-1-1-44000022-2-20000000000000000000002-200-1-1110000000000000000
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χ52444-24-24444-2-24-2-2-21-2-2-2-2-2-2-2-2-21-2-2-244-2-2-2-21111111-2-2111110044000000-2-20000-2-2000000000000-200110000-2110000000000000
χ53444-24-24444-2-24-2-2-21-2-2-2-2-2-2-2-2-21-2-2-244-2-2-2-21111111-2-21111100-4-400000022000022000000000000200-1-100002-1-10000000000000
χ54444-24-2-4-444-2-2422-21-2-2-2-2-2-2-2-2-21222-4-42222-1-11111122-1-1-1-1-10000000000−2i32i30000−2i32i3000000000000000i3−i300000i3−i30000000000000
χ55444-24-2-4-444-2-2422-21-2-2-2-2-2-2-2-2-21222-4-42222-1-11111122-1-1-1-1-100000000002i3−2i300002i3−2i3000000000000000−i3i300000−i3i30000000000000
χ56444-2-2444-2-2-24-2-2-21-2-24-2-21-2-211-2-244-2-21111-2-21-2111-2-2-21111000044000000-2-2-2-200-2-2-2-2111111110000000000000000000000000
χ57444-2-2444-2-2-24-2-2-21-2-24-2-21-2-211-2-244-2-21111-2-21-2111-2-2-211110000-4-40000002222002222-1-1-1-1-1-1-1-10000000000000000000000000
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χ988-808-4-400−4i34i3-84400-4-4202i3−2i34-20−4i34i3400000000000202i3−2i3-200000000000000000000000000000000000000000000000000000000000000
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χ1058-80-4-4-4004i3−4i3444−43432220−2i32i3-2-20−2i32i3-20000023−236i−6i23−23-10i3−i31000−33−3i3i0000000000000000000000000000000000000000000000000000000

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