Finite Group Databasebeta

← Group #13155924

Character table — Group #13155924

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size11222222222222244444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212242424242424242424242424363636363636727272727272216
order12233344666121212123336666666612121212121212121212121236666612121212121222444466661212121212121212121212121212121212121212666666121212121212441212121288242424242
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-11-11111-1-111-1-111111111111111111-111-1-11-111-1-1-1-1-1-1-1-11-111-1-1-1
χ4111111111111111111111111111111111111111111111111111-11-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-1-1-1-1-1-1-1-11-1-1111
χ511111111111111111111111111111111111111111111111111-11-1111-1-111-1-1111111111111111111-11-1-111-11-1-111-1-1-1-1-1-1-11-1-111-1
χ611111111111111111111111111111111111111111111111111-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-111-1-1-1-1-1-11-111-1-11
χ711111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11
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
χ9222222-2-2222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000000000000000002-222-2-20000000
χ10222222-2-2222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000000000-22-2-2220000000
χ1122222-12222-122222-1-1-122222-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200-1-1-1-1-1-1-1-1000000000000000022-1-1-1-122-1-1-1-122-1-1-1-10000000
χ1222222-12222-122222-1-1-122222-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-22-200-1-111-1-11100000000000000002-2-1-1112-2-1-111-2-211110000000
χ1322222-12222-122222-1-1-122222-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22-220011-1-111-1-10000000000000000-2211-1-1-2211-1-1-2-211110000000
χ1422222-12222-122222-1-1-122222-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200111111110000000000000000-2-21111-2-2111122-1-1-1-10000000
χ1522222-1-2-222-1-2-2-2-22-1-1-122222-1-1-2-211-2-2-2-21111-1-1-1-1-1-1111111000000−i3i3−i3i3−i3i3−i3i3000000000000000000−i3i3−i3i300−i3i3−i3i32-2-1-1110000000
χ1622222-1-2-222-1-2-2-2-22-1-1-122222-1-1-2-211-2-2-2-21111-1-1-1-1-1-1111111000000−i3i3i3−i3−i3i3i3−i3000000000000000000−i3i3i3−i300−i3i3i3−i3-2211-1-10000000
χ1722222-1-2-222-1-2-2-2-22-1-1-122222-1-1-2-211-2-2-2-21111-1-1-1-1-1-1111111000000i3−i3−i3i3i3−i3−i3i3000000000000000000i3−i3−i3i300i3−i3−i3i3-2211-1-10000000
χ1822222-1-2-222-1-2-2-2-22-1-1-122222-1-1-2-211-2-2-2-21111-1-1-1-1-1-1111111000000i3−i3i3−i3i3−i3i3−i3000000000000000000i3−i3i3−i300i3−i3i3−i32-2-1-1110000000
χ192222-12222-1222-1-1-12-12-12-1-1-12-12-122-1-1-1-122-1-1-12-1-1-1-12-1-1-1-1-1020222002200222222-1-1-1-1-1-1-1-1-1-1-1-10-100-1-10-100-1-10000000200-1-10
χ202222-12222-1222-1-1-12-12-12-1-1-12-12-122-1-1-1-122-1-1-12-1-1-1-12-1-1-1-1-10202-2-200220022-2-2-2-21111111111110-100-1-10-100-1-10000000-200110
χ212222-12222-1222-1-1-12-12-12-1-1-12-12-122-1-1-1-122-1-1-12-1-1-1-12-1-1-1-1-10-20-22200-2-200-2-22222-1-1-1-1-1-1-1-1-1-1-1-10100110100110000000-200110
χ222222-12222-1222-1-1-12-12-12-1-1-12-12-122-1-1-1-122-1-1-12-1-1-1-12-1-1-1-1-10-20-2-2-200-2-200-2-2-2-2-2-21111111111110100110100110000000200-1-10
χ23222-12222-122-1-122-1-122-1-12-1-1-12-1222-1-1-1-1-1-122-1-12-1-1-1-12-1-1-1-120202222002200-1-1-1-12222-1-1-1-1-1-1-1-1-10-1-100-10-1-10000000020-1-1000
χ24222-12222-122-1-122-1-122-1-12-1-1-12-1222-1-1-1-1-1-122-1-12-1-1-1-12-1-1-1-12020-2-2220022001111-2-2-2-211111111-10-1-100-10-1-100000000-2011000
χ25222-12222-122-1-122-1-122-1-12-1-1-12-1222-1-1-1-1-1-122-1-12-1-1-1-12-1-1-1-1-20-2022-2-200-2-200-1-1-1-12222-1-1-1-1-1-1-1-1101100101100000000-2011000
χ26222-12222-122-1-122-1-122-1-12-1-1-12-1222-1-1-1-1-1-122-1-12-1-1-1-12-1-1-1-1-20-20-2-2-2-200-2-2001111-2-2-2-21111111110110010110000000020-1-1000
χ2722-22222-222222-2-2222-22-2-2-2-222-222-222-2-222-2-22-2-2-2-22-2222-2-2020-200002200-2-200000000000000000200220-200-2-20000000000000
χ2822-22222-222222-2-2222-22-2-2-2-222-222-222-2-222-2-22-2-2-2-22-2222-2-20-2020000-2-2002200000000000000000-200-2-20200220000000000000
χ2922-2222-22222-2-222222-22-2-2-2-2222-2-22-2-222-2-2222-2-2-2-222-2-2-22220-20002200-2-2000000000000000000202200-20-2-2000000000000000
χ3022-2222-22222-2-222222-22-2-2-2-2222-2-22-2-222-2-2222-2-2-2-222-2-2-222-202000-2-20022000000000000000000-20-2-2002022000000000000000
χ3122-222-12-222-122-2-22-1-112-2-2-2-2-1-1-22-1122-2-2-1-111-11111-11-1-1-111020-200−i3i3-1-1i3−i311000000000000000002−i3i3-1-10-2i3−i31100−i3i3−i3i30000000
χ3222-222-12-222-122-2-22-1-112-2-2-2-2-1-1-22-1122-2-2-1-111-11111-11-1-1-111020-200i3−i3-1-1−i3i311000000000000000002i3−i3-1-10-2−i3i31100i3−i3i3−i30000000
χ3322-222-12-222-122-2-22-1-112-2-2-2-2-1-1-22-1122-2-2-1-111-11111-11-1-1-1110-20200−i3i311i3−i3-1-100000000000000000-2−i3i31102i3−i3-1-100i3−i3i3−i30000000
χ3422-222-12-222-122-2-22-1-112-2-2-2-2-1-1-22-1122-2-2-1-111-11111-11-1-1-1110-20200i3−i311−i3i3-1-100000000000000000-2i3−i31102−i3i3-1-100−i3i3−i3i30000000
χ3522-222-1-2222-1-2-2222-1-112-2-2-2-2-1-12-21-1-2-22211-1-1-11111-1-1111-1-120-2000-1-1−i3i311i3−i3000000000000000020-1-1−i3i3-2011i3−i300−i3i3i3−i30000000
χ3622-222-1-2222-1-2-2222-1-112-2-2-2-2-1-12-21-1-2-22211-1-1-11111-1-1111-1-120-2000-1-1i3−i311−i3i3000000000000000020-1-1i3−i3-2011−i3i300i3−i3−i3i30000000
χ3722-222-1-2222-1-2-2222-1-112-2-2-2-2-1-12-21-1-2-22211-1-1-11111-1-1111-1-1-20200011−i3i3-1-1i3−i30000000000000000-2011−i3i320-1-1i3−i300i3−i3−i3i30000000
χ3822-222-1-2222-1-2-2222-1-112-2-2-2-2-1-12-21-1-2-22211-1-1-11111-1-1111-1-1-20200011i3−i3-1-1−i3i30000000000000000-2011i3−i320-1-1−i3i300−i3i3i3−i30000000
χ3922-22-122-22-122211-12-1-2-1-21112-1-2-12-2-1-1112211-1-2111-1-2-1-1-111020-200002200-2-2000033−3−33333−3−3−3−30-100-1-101001100000000003−30
χ4022-22-122-22-122211-12-1-2-1-21112-1-2-12-2-1-1112211-1-2111-1-2-1-1-111020-200002200-2-20000−3−333−3−3−3−333330-100-1-10100110000000000−330
χ4122-22-122-22-122211-12-1-2-1-21112-1-2-12-2-1-1112211-1-2111-1-2-1-1-1110-2020000-2-20022000033−3−33333−3−3−3−30100110-100-1-10000000000−330
χ4222-22-122-22-122211-12-1-2-1-21112-1-2-12-2-1-1112211-1-2111-1-2-1-1-1110-2020000-2-200220000−3−333−3−3−3−333330100110-100-1-100000000003−30
χ4322-2-122-22-1221122-1-12-2-11-211-12-1-2-2211-1-11122-11-211-1-1-211-1-120-20002200-2-20033−3−3000033−3−333−3−3-10-1-100101100000000003−3000
χ4422-2-122-22-1221122-1-12-2-11-211-12-1-2-2211-1-11122-11-211-1-1-211-1-120-20002200-2-200−3−3330000−3−333−3−333-10-1-10010110000000000−33000
χ4522-2-122-22-1221122-1-12-2-11-211-12-1-2-2211-1-11122-11-211-1-1-211-1-1-202000-2-200220033−3−3000033−3−333−3−3101100-10-1-10000000000−33000
χ4622-2-122-22-1221122-1-12-2-11-211-12-1-2-2211-1-11122-11-211-1-1-211-1-1-202000-2-2002200−3−3330000−3−333−3−333101100-10-1-100000000003−3000
χ474444-24-4-44-24-4-422-24-24-24-2-2-24-2-42-4-42222-4-422-24-2-2-2-2-4222220000000000000000000000000000000000000000000000000000000
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χ494444-2-2444-2-244-2-2-2-21-2-24-2-2-2-214-2-2-2-2-2-2-2-2-2111-21111-2111110-40-4000022002200000000000000000200-1-10200-1-10000000000000
χ504444-2-2-4-44-2-2-4-422-2-21-2-24-2-2-2-21-4222222222-1-11-211112-1-1-1-1-100000000−2i32i300−2i32i300000000000000000000i3−i30000i3−i30000000000000
χ514444-2-2-4-44-2-2-4-422-2-21-2-24-2-2-2-21-4222222222-1-11-211112-1-1-1-1-1000000002i3−2i3002i3−2i300000000000000000000−i3i30000−i3i30000000000000
χ52444-244-4-4-24422-4-4-2-244-2-24-2-2-242-4-4-4222222-4-4-2-24-2-2-22-422220000000000000000000000000000000000000000000000000000000
χ53444-24-244-24-2-2-244-21-2-2-2-24-2-21-2-24-2-2-2-2-2-211-2-211-21111-21111404000-2-200-2-2000000000000000000-201100-2011000000000000000
χ54444-24-244-24-2-2-244-21-2-2-2-24-2-21-2-24-2-2-2-2-2-211-2-211-21111-21111-40-400022002200000000000000000020-1-10020-1-1000000000000000
χ55444-24-2-4-4-24-222-4-4-21-2-2-2-24-2-21-22-4222222-1-12211-2111-12-1-1-1-1000000−2i32i300−2i32i300000000000000000000i3−i30000i3−i3000000000000000
χ56444-24-2-4-4-24-222-4-4-21-2-2-2-24-2-21-22-4222222-1-12211-2111-12-1-1-1-10000002i3−2i3002i3−2i300000000000000000000−i3i30000−i3i3000000000000000
χ57444-2-2444-2-24-2-2-2-21-2-241-2-211-2-2-2-2441111-2-2-2-21-2-2111-2-2111100004400000000-2-2-2-2-2-2-2-2111111110000000000000000000000000
χ58444-2-2444-2-24-2-2-2-21-2-241-2-211-2-2-2-2441111-2-2-2-21-2-2111-2-211110000-4-40000000022222222-1-1-1-1-1-1-1-10000000000000000000000000
χ59444-2-24-4-4-2-2422221-2-241-2-211-2-222-4-4-1-1-1-122221-2-211122-1-1-1-1000000000000000000000033-3-3-3-3330000000000000000000000000
χ60444-2-24-4-4-2-2422221-2-241-2-211-2-222-4-4-1-1-1-122221-2-211122-1-1-1-10000000000000000000000-3-33333-3-30000000000000000000000000
χ6144-44-24-444-24-4-4-2-2-24-2-4-2-42224-242-4422-2-2-4-4-2-2-2-4222-24222-2-20000000000000000000000000000000000000000000000000000000
χ6244-44-2-24-44-2-24422-2-212-2-4222-21-4-2-22-2-222-2-2-1-112-1-1-112111-1-1040-40000-2-2002200000000000000000-200110200-1-10000000000000
χ6344-44-2-24-44-2-24422-2-212-2-4222-21-4-2-22-2-222-2-2-1-112-1-1-112111-1-10-40400002200-2-200000000000000000200-1-10-200110000000000000
χ6444-44-2-2-444-2-2-4-4-2-2-2-212-2-4222-21422-222-2-2221112-1-1-11-2-1-1-11100000000−2i32i3002i3−2i300000000000000000000i3−i30000−i3i30000000000000
χ6544-44-2-2-444-2-2-4-4-2-2-2-212-2-4222-21422-222-2-2221112-1-1-11-2-1-1-111000000002i3−2i300−2i32i300000000000000000000−i3i30000i3−i30000000000000
χ6644-4-2444-4-244-2-2-4-4-2-24-4-22-422-24244-4-2-222-2-2-4-4-22-422-224-2-2220000000000000000000000000000000000000000000000000000000
χ6744-4-24-24-4-24-2-2-2-4-4-21-22-22-4221-224-22-2-22211221-12-1-11-1-211-1-1000000−2i32i3002i3−2i300000000000000000000i3−i30000−i3i3000000000000000
χ6844-4-24-24-4-24-2-2-2-4-4-21-22-22-4221-224-22-2-22211221-12-1-11-1-211-1-10000002i3−2i300−2i32i300000000000000000000−i3i30000i3−i3000000000000000
χ6944-4-24-2-44-24-22244-21-22-22-4221-2-2-42-222-2-2-1-1-2-21-12-1-1112-1-11140-4000-2-20022000000000000000000-20110020-1-1000000000000000
χ7044-4-24-2-44-24-22244-21-22-22-4221-2-2-42-222-2-2-1-1-2-21-12-1-1112-1-111-4040002200-2-200000000000000000020-1-100-2011000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.