Finite Group Databasebeta

← Group #11772557

Character table — Group #11772557

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112244444444444444444444444444444444444444444444444444444444444444444444443636363672727272727272727272
order12222222334444666666666666666666666666666666121212121212121212121212121212121212121212121212121212121212121222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1−i−iii−i−iii
χ51111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ61111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii
χ81111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i
χ91-1-111-11-111ii−i−i11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1-1-11i−ii−ii−i1-11-1
χ101-1-111-11-111ii−i−i11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i1-1-11i−i−ii−ii-11-11
χ111-1-111-11-111ii−i−i11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-111-1−ii1-1-11−iii−i
χ121-1-111-11-111ii−i−i11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-111-1−ii-111-1i−i−ii
χ131-1-111-11-111−i−iii11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii1-1-11−iii−ii−i-11-11
χ141-1-111-11-111−i−iii11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii1-1-11−ii−ii−ii1-11-1
χ151-1-111-11-111−i−iii11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-111-1i−i1-1-11i−i−ii
χ161-1-111-11-111−i−iii11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-111-1i−i-111-1−iii−i
χ17222222-2-2220000222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2220000000000000000000000000000000022-2-20000000000
χ18222222-2-2220000222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22200000000000000000000000000000000-2-2220000000000
χ192-2-222-2-22220000222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2000000000000000000000000000000002-22-20000000000
χ202-2-222-2-22220000222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-200000000000000000000000000000000-22-220000000000
χ21444444441-24444111-2-2-21111-2-2-2-2111-2-2-21111-2-2-2-21-211111111-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-200000000000000
χ22444444441-2-4-4-4-4111-2-2-21111-2-2-2-2111-2-2-21111-2-2-2-21-2-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222222200000000000000
χ2344444444-214444-2-2-2111-2-2-2-21111-2-2-2111-2-2-2-21111-21-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-21111111100000000000000
χ2444444444-21-4-4-4-4-2-2-2111-2-2-2-21111-2-2-2111-2-2-2-21111-2122222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-100000000000000
χ25444444-4-41-20000111-2-2-2-1-1-1-12222111-2-2-2-1-1-1-122221-23333-3-3-3-3000000003333-3-3-3-30000000000000000000000
χ26444444-4-41-20000111-2-2-2-1-1-1-12222111-2-2-2-1-1-1-122221-2-3-3-3-3333300000000-3-3-3-333330000000000000000000000
χ27444444-4-4-210000-2-2-21112222-1-1-1-1-2-2-21112222-1-1-1-1-21000000003333-3-3-3-3000000003333-3-3-3-300000000000000
χ28444444-4-4-210000-2-2-21112222-1-1-1-1-2-2-21112222-1-1-1-1-2100000000-3-3-3-3333300000000-3-3-3-3333300000000000000
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χ3944-4-400001-22i−2i2i−2i-13-3002i3−i3i3−i3002i3−2i313-300-2i3−i3i3−i3002i3−2i3-12i−ii−i−ζ7−3ζ11ζ7+3ζ113ζ7+ζ11−3ζ7−ζ11−2ζ112ζ112ζ7−2ζ72ζ7−2ζ7−2ζ112ζ11i−ii−i−ζ7−3ζ11ζ7+3ζ113ζ7+ζ11−3ζ7−ζ11−2ζ112ζ112ζ7−2ζ72ζ7−2ζ7−2ζ112ζ1100000000000000
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χ4144-4-400001-22i−2i2i−2i-1-33002i3−i3−i3i32i3−2i3001-3300-2i3−i3−i3i32i3−2i300-123ζ7+ζ11−3ζ7−ζ11ζ7+3ζ11−ζ7−3ζ11−iii−i−2ζ112ζ112ζ7−2ζ72ζ11−2ζ11−2ζ72ζ73ζ7+ζ11−3ζ7−ζ11ζ7+3ζ11−ζ7−3ζ11−iii−i−2ζ112ζ112ζ7−2ζ72ζ11−2ζ11−2ζ72ζ700000000000000
χ4244-4-400001-2−2i2i−2i2i-13-3002−i3i3−i3i300−2i32i313-300-2−i3i3−i3i300−2i32i3-12−ii−ii3ζ7+ζ11−3ζ7−ζ11−ζ7−3ζ11ζ7+3ζ112ζ7−2ζ7−2ζ112ζ11−2ζ112ζ112ζ7−2ζ7−ii−ii3ζ7+ζ11−3ζ7−ζ11−ζ7−3ζ11ζ7+3ζ112ζ7−2ζ7−2ζ112ζ11−2ζ112ζ112ζ7−2ζ700000000000000
χ4344-4-400001-2−2i2i−2i2i-13-3002i3−i3i3−i3002i3−2i313-300-2i3−i3i3−i3002i3−2i3-12−ii−iiζ7+3ζ11−ζ7−3ζ11−3ζ7−ζ113ζ7+ζ112ζ11−2ζ11−2ζ72ζ7−2ζ72ζ72ζ11−2ζ11−ii−iiζ7+3ζ11−ζ7−3ζ11−3ζ7−ζ113ζ7+ζ112ζ11−2ζ11−2ζ72ζ7−2ζ72ζ72ζ11−2ζ1100000000000000
χ4444-4-400001-2−2i2i−2i2i-1-33002−i3i3i3−i3−2i32i3001-3300-2−i3i3i3−i3−2i32i300-12−ζ7−3ζ11ζ7+3ζ11−3ζ7−ζ113ζ7+ζ11i−i−ii2ζ7−2ζ7−2ζ112ζ11−2ζ72ζ72ζ11−2ζ11−ζ7−3ζ11ζ7+3ζ11−3ζ7−ζ113ζ7+ζ11i−i−ii2ζ7−2ζ7−2ζ112ζ11−2ζ72ζ72ζ11−2ζ1100000000000000
χ4544-4-400001-2−2i2i−2i2i-1-33002i3−i3−i3i32i3−2i3001-3300-2i3−i3−i3i32i3−2i300-12−3ζ7−ζ113ζ7+ζ11−ζ7−3ζ11ζ7+3ζ11i−i−ii2ζ11−2ζ11−2ζ72ζ7−2ζ112ζ112ζ7−2ζ7−3ζ7−ζ113ζ7+ζ11−ζ7−3ζ11ζ7+3ζ11i−i−ii2ζ11−2ζ11−2ζ72ζ7−2ζ112ζ112ζ7−2ζ700000000000000
χ4644-4-40000442i−2i2i−2i-40000-40000000040000400000000-4-4−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i00000000000000
χ4744-4-4000044−2i2i−2i2i-40000-40000000040000400000000-4-42i−2i2i−2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i2i−2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000000000
χ4844-4-40000-212i−2i2i−2i2003-3-100−2i32i3−i3i3i3−i3-2003-3100−2i32i3−i3i3i3−i32-1−2ζ112ζ11−2ζ72ζ72ζ11−2ζ11−2ζ72ζ7i−i−ii−ζ7−3ζ11ζ7+3ζ113ζ7+ζ11−3ζ7−ζ11−2ζ112ζ11−2ζ72ζ72ζ11−2ζ11−2ζ72ζ7i−i−ii−ζ7−3ζ11ζ7+3ζ113ζ7+ζ11−3ζ7−ζ1100000000000000
χ4944-4-40000-212i−2i2i−2i2003-3-1002i3−2i3i3−i3−i3i3-2003-31002i3−2i3i3−i3−i3i32-1−2ζ72ζ7−2ζ112ζ112ζ7−2ζ7−2ζ112ζ11i−i−ii−3ζ7−ζ113ζ7+ζ11ζ7+3ζ11−ζ7−3ζ11−2ζ72ζ7−2ζ112ζ112ζ7−2ζ7−2ζ112ζ11i−i−ii−3ζ7−ζ113ζ7+ζ11ζ7+3ζ11−ζ7−3ζ1100000000000000
χ5044-4-40000-212i−2i2i−2i200-33-1−2i32i300i3−i3i3−i3-200-331−2i32i300i3−i3i3−i32-1−2ζ72ζ7−2ζ112ζ112ζ11−2ζ11−2ζ72ζ73ζ7+ζ11−3ζ7−ζ11−ζ7−3ζ11ζ7+3ζ11−iii−i−2ζ72ζ7−2ζ112ζ112ζ11−2ζ11−2ζ72ζ73ζ7+ζ11−3ζ7−ζ11−ζ7−3ζ11ζ7+3ζ11−iii−i00000000000000
χ5144-4-40000-212i−2i2i−2i200-33-12i3−2i300−i3i3−i3i3-200-3312i3−2i300−i3i3−i3i32-1−2ζ112ζ11−2ζ72ζ72ζ7−2ζ7−2ζ112ζ11ζ7+3ζ11−ζ7−3ζ11−3ζ7−ζ113ζ7+ζ11−iii−i−2ζ112ζ11−2ζ72ζ72ζ7−2ζ7−2ζ112ζ11ζ7+3ζ11−ζ7−3ζ11−3ζ7−ζ113ζ7+ζ11−iii−i00000000000000
χ5244-4-40000-21−2i2i−2i2i2003-3-100−2i32i3−i3i3i3−i3-2003-3100−2i32i3−i3i3i3−i32-12ζ11−2ζ112ζ7−2ζ7−2ζ112ζ112ζ7−2ζ7−iii−iζ7+3ζ11−ζ7−3ζ11−3ζ7−ζ113ζ7+ζ112ζ11−2ζ112ζ7−2ζ7−2ζ112ζ112ζ7−2ζ7−iii−iζ7+3ζ11−ζ7−3ζ11−3ζ7−ζ113ζ7+ζ1100000000000000
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χ654-44-4000044-222-2-40000-400000000-40000-400000000442-22-2-222-22-2-22-222-2-22-222-2-22-222-22-2-2200000000000000
χ664-44-40000-212-2-222003-3-100−2i32i3−i3i3i3−i3200-33-1002i3−2i3i3−i3−i3i3-211+i3−1−i31−i3−1+i3−1−i31+i31−i3−1+i31-1-112+i3−2−i3−2+i32−i3−1−i31+i3−1+i31−i31+i3−1−i3−1+i31−i3-111-1−2−i32+i32−i3−2+i300000000000000
χ674-44-40000-212-2-222003-3-1002i3−2i3i3−i3−i3i3200-33-100−2i32i3−i3i3i3−i3-211−i3−1+i31+i3−1−i3−1+i31−i31+i3−1−i31-1-112−i3−2+i3−2−i32+i3−1+i31−i3−1−i31+i31−i3−1+i3−1−i31+i3-111-1−2+i32−i32+i3−2−i300000000000000
χ684-44-40000-212-2-22200-33-1−2i32i300i3−i3i3−i32003-3-12i3−2i300−i3i3−i3i3-211−i3−1+i31+i3−1−i3−1−i31+i31−i3−1+i3−2+i32−i32+i3−2−i3-111-1−1+i31−i3−1−i31+i31+i3−1−i3−1+i31−i32−i3−2+i3−2−i32+i31-1-1100000000000000
χ694-44-40000-212-2-22200-33-12i3−2i300−i3i3−i3i32003-3-1−2i32i300i3−i3i3−i3-211+i3−1−i31−i3−1+i3−1+i31−i31+i3−1−i3−2−i32+i32−i3−2+i3-111-1−1−i31+i3−1+i31−i31−i3−1+i3−1−i31+i32+i3−2−i3−2+i32−i31-1-1100000000000000
χ704-44-40000-21-222-22003-3-100−2i32i3−i3i3i3−i3200-33-1002i3−2i3i3−i3−i3i3-21−1−i31+i3−1+i31−i31+i3−1−i3−1+i31−i3-111-1−2−i32+i32−i3−2+i31+i3−1−i31−i3−1+i3−1−i31+i31−i3−1+i31-1-112+i3−2−i3−2+i32−i300000000000000
χ714-44-40000-21-222-22003-3-1002i3−2i3i3−i3−i3i3200-33-100−2i32i3−i3i3i3−i3-21−1+i31−i3−1−i31+i31−i3−1+i3−1−i31+i3-111-1−2+i32−i32+i3−2−i31−i3−1+i31+i3−1−i3−1+i31−i31+i3−1−i31-1-112−i3−2+i3−2−i32+i300000000000000
χ724-44-40000-21-222-2200-33-1−2i32i300i3−i3i3−i32003-3-12i3−2i300−i3i3−i3i3-21−1+i31−i3−1−i31+i31+i3−1−i3−1+i31−i32−i3−2+i3−2−i32+i31-1-111−i3−1+i31+i3−1−i3−1−i31+i31−i3−1+i3−2+i32−i32+i3−2−i3-111-100000000000000
χ734-44-40000-21-222-2200-33-12i3−2i300−i3i3−i3i32003-3-1−2i32i300i3−i3i3−i3-21−1−i31+i3−1+i31−i31−i3−1+i3−1−i31+i32+i3−2−i3−2+i32−i31-1-111+i3−1−i31−i3−1+i3−1+i31−i31+i3−1−i3−2−i32+i32−i3−2+i3-111-100000000000000
χ744-4-444-44-41-24i4i−4i−4i111-2-2-21111-2-2-2-2-1-1-1222-1-1-1-12222-12iiiiiiii−2i−2i−2i−2i−2i−2i−2i−2i−i−i−i−i−i−i−i−i2i2i2i2i2i2i2i2i00000000000000
χ754-4-444-44-41-2−4i−4i4i4i111-2-2-21111-2-2-2-2-1-1-1222-1-1-1-12222-12−i−i−i−i−i−i−i−i2i2i2i2i2i2i2i2iiiiiiiii−2i−2i−2i−2i−2i−2i−2i−2i00000000000000
χ764-4-444-44-4-214i4i−4i−4i-2-2-2111-2-2-2-21111222-1-1-12222-1-1-1-12-1−2i−2i−2i−2i−2i−2i−2i−2iiiiiiiii2i2i2i2i2i2i2i2i−i−i−i−i−i−i−i−i00000000000000
χ774-4-444-44-4-21−4i−4i4i4i-2-2-2111-2-2-2-21111222-1-1-12222-1-1-1-12-12i2i2i2i2i2i2i2i−i−i−i−i−i−i−i−i−2i−2i−2i−2i−2i−2i−2i−2iiiiiiiii00000000000000
χ784-4-444-4-441-20000111-2-2-2-1-1-1-12222-1-1-12221111-2-2-2-2-123i3i3i3i−3i−3i−3i−3i00000000−3i−3i−3i−3i3i3i3i3i0000000000000000000000
χ794-4-444-4-441-20000111-2-2-2-1-1-1-12222-1-1-12221111-2-2-2-2-12−3i−3i−3i−3i3i3i3i3i000000003i3i3i3i−3i−3i−3i−3i0000000000000000000000
χ804-4-444-4-44-210000-2-2-21112222-1-1-1-1222-1-1-1-2-2-2-211112-1000000003i3i3i3i−3i−3i−3i−3i00000000−3i−3i−3i−3i3i3i3i3i00000000000000
χ814-4-444-4-44-210000-2-2-21112222-1-1-1-1222-1-1-1-2-2-2-211112-100000000−3i−3i−3i−3i3i3i3i3i000000003i3i3i3i−3i−3i−3i−3i00000000000000
χ824-4-44-44001-200001-1-122-233-3-30000-111-2-22-3-3330000-1233−3−333−3−300002323−23−23−3−333−3−3330000−23−23232300000000000000
χ834-4-44-44001-200001-1-122-233-3-30000-111-2-22-3-3330000-12−3−333−3−3330000−23−23232333−3−333−3−300002323−23−2300000000000000
χ844-4-44-44001-200001-1-122-2-3-3330000-111-2-2233-3-30000-1233−3−3−3−3332323−23−230000−3−33333−3−3−23−232323000000000000000000
χ854-4-44-44001-200001-1-122-2-3-3330000-111-2-2233-3-30000-12−3−33333−3−3−23−232323000033−3−3−3−3332323−23−23000000000000000000
χ864-4-44-44004400004-4-4-4-4400000000-44444-400000000-4-40000000000000000000000000000000000000000000000
χ874-4-44-4400-210000-222-1-11000033-3-32-2-211-10000-3-3332-100002323−23−2333−3−3−3−3330000−23−232323−3−33333−3−300000000000000
χ884-4-44-4400-210000-222-1-11000033-3-32-2-211-10000-3-3332-10000−23−232323−3−33333−3−300002323−23−2333−3−3−3−33300000000000000
χ894-4-44-4400-210000-222-1-110000-3-3332-2-211-1000033-3-32-12323−23−230000−3−333−3−333−23−232323000033−3−333−3−300000000000000
χ904-4-44-4400-210000-222-1-110000-3-3332-2-211-1000033-3-32-1−23−232323000033−3−333−3−32323−23−230000−3−333−3−33300000000000000

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