Finite Group Databasebeta

← Group #13155749

Character table — Group #13155749

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444444444448888888888881212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636365454545472727272
order1244233346661212121212123336666666612121212121212121212123666661212121212122488882424242424242424242424242424242466661212121224242424242424242444881212121288886122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ51111111111111111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ911-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-11-1-1-1-111111-1-11-1i−i1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1i−ii−iii−i−i1-1i−ii−iii−i−iii−i−i1-1i−i
χ1011-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-11-1-1-1-111111-1-11-1i−i-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1i−ii−iii−i−i-11i−i−iiii−i−i−i−iii-11−ii
χ1111-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-11-1-1-1-111111-1-11-1−ii1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1−ii−ii−i−iii1-1−ii−ii−i−iii−i−iii1-1−ii
χ1211-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-11-1-1-1-111111-1-11-1−ii-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1−ii−ii−i−iii-11−iii−i−i−iiiii−i−i-11i−i
χ1311-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-11-1-1-1-111111-1-1-11i−i1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−iii−i−i-11−iii−i−i−iii−i−iii-11i−i
χ1411-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-11-1-1-1-111111-1-1-11i−i-11-1-1-1-1-1-1-1-111111111-1-1-1-11111i−ii−iii−i−i1-1−ii−ii−i−iiiii−i−i1-1−ii
χ1511-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-11-1-1-1-111111-1-1-11−ii1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111−ii−ii−i−iii-11i−i−iiii−i−iii−i−i-11−ii
χ1611-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-11111-1-11-1-1-1-111111-1-1-11−ii-11-1-1-1-1-1-1-1-111111111-1-1-1-11111−ii−ii−i−iii1-1i−ii−iii−i−i−i−iii1-1i−i
χ172222222-1222-1-1-122222-1-12-1-1-12-1-122-1-1-1-12-1-1-122-12-1-1-1-12-1-1-1-1-122002222-1-1-1-1-1-122-1-1-1-1-1-12-1-1-12-1-1-10000000022000000000000-1-100
χ182222222-1222-1-1-122222-1-12-1-1-12-1-122-1-1-1-12-1-1-122-12-1-1-1-12-1-1-1-1-12200-2-2-2-2111111-2-21111112-1-1-12-1-1-100000000-2-20000000000001100
χ192222222-1222-1-1-122222-1-12-1-1-12-1-122-1-1-1-12-1-1-122-12-1-1-1-12-1-1-1-1-1-2-2002222-1-1-1-1-1-122-1-1-1-1-1-1-2111-211100000000-2-20000000000001100
χ202222222-1222-1-1-122222-1-12-1-1-12-1-122-1-1-1-12-1-1-122-12-1-1-1-12-1-1-1-1-1-2-200-2-2-2-2111111-2-2111111-2111-21110000000022000000000000-1-100
χ21222222-1222-1222-1-122-12-12222-12-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000000-12-1-1-12-1-1-1-122-1-1-1-1002200-1-1-1-100000000
χ22222222-1222-1222-1-122-12-12222-12-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2000000000000000000-12-1-1-12-1-111-2-2111100-2-200111100000000
χ23222222-1222-1222-1-122-12-12222-12-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000000000000000001-2111-211-1-122-1-1-1-100-2-200111100000000
χ24222222-1222-1222-1-122-12-12222-12-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000001-2111-21111-2-21111002200-1-1-1-100000000
χ2522222-1222-1222222-1-1-1-12-12-1-1-1-1222-1-122-12-1-1-1-1-1-12-1-1-1-12-1-1-1-1002222-1-122-1-1-1-1-1-122-1-1-1-10000000022-1-1-1-1-1-10000220000000000-1-1
χ2622222-1222-1222222-1-1-1-12-12-1-1-1-1222-1-122-12-1-1-1-1-1-12-1-1-1-12-1-1-1-10022-2-211-2-2111111-2-211110000000022-1-1-1-1-1-10000-2-2000000000011
χ2722222-1222-1222222-1-1-1-12-12-1-1-1-1222-1-122-12-1-1-1-1-1-12-1-1-1-12-1-1-1-100-2-222-1-122-1-1-1-1-1-122-1-1-1-100000000-2-21111110000-2-2000000000011
χ2822222-1222-1222222-1-1-1-12-12-1-1-1-1222-1-122-12-1-1-1-1-1-12-1-1-1-12-1-1-1-100-2-2-2-211-2-2111111-2-2111100000000-2-21111110000220000000000-1-1
χ292222-2222-2222222222222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-22-2-2-2-2220000000000000000000000000000000000000000000000002-22-20000
χ302222-2222-2222222222222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-22-2-2-2-222000000000000000000000000000000000000000000000000-22-220000
χ3122-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ3222-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ3322-2-2-222-1222-111-2-2-2-22-1-1-21112-1-1-2211112-1-1-1-2-2-1-2111-12-1-1-1112-2002-222-1-1-1-1-1-1-2-21111112-1-1-1-2111000000002-2000000000000-1100
χ3422-2-2-222-1222-111-2-2-2-22-1-1-21112-1-1-2211112-1-1-1-2-2-1-2111-12-1-1-1112-200-22-2-211111122-1-1-1-1-1-12-1-1-1-211100000000-220000000000001-100
χ3522-2-2-222-1222-111-2-2-2-22-1-1-21112-1-1-2211112-1-1-1-2-2-1-2111-12-1-1-111-22002-222-1-1-1-1-1-1-2-2111111-21112-1-1-100000000-220000000000001-100
χ3622-2-2-222-1222-111-2-2-2-22-1-1-21112-1-1-2211112-1-1-1-2-2-1-2111-12-1-1-111-2200-22-2-211111122-1-1-1-1-1-1-21112-1-1-1000000002-2000000000000-1100
χ3722-2-2-22-1222-12-2-211-2-2-12-1-2-2-2-2-12-11-1-2-211222211-11111-1-1-1-1-1112-22i−2i000000000000000000-12-1-11-211−ii2i−2i−i−iii002i−2i00−i−iii00000000
χ3822-2-2-22-1222-12-2-211-2-2-12-1-2-2-2-2-12-11-1-2-211222211-11111-1-1-1-1-1112-2−2i2i000000000000000000-12-1-11-211i−i−2i2iii−i−i00−2i2i00ii−i−i00000000
χ3922-2-2-22-1222-12-2-211-2-2-12-1-2-2-2-2-12-11-1-2-211222211-11111-1-1-1-1-111-222i−2i0000000000000000001-211-12-1-1−ii2i−2i−i−iii00−2i2i00ii−i−i00000000
χ4022-2-2-22-1222-12-2-211-2-2-12-1-2-2-2-2-12-11-1-2-211222211-11111-1-1-1-1-111-22−2i2i0000000000000000001-211-12-1-1i−i−2i2iii−i−i002i−2i00−i−iii00000000
χ4122-2-2-2-1222-122-2-2-2-211-1-121-211-1-12-2211-2-2-12-1-111-11-211-1-12-1-111002i−2i2-2-1-122-1-1-1-111-2-21111000000002i−2i−ii−i−iii00002i−2i0000000000−ii
χ4222-2-2-2-1222-122-2-2-2-211-1-121-211-1-12-2211-2-2-12-1-111-11-211-1-12-1-111002i−2i-2211-2-21111-1-122-1-1-1-1000000002i−2i−ii−i−iii0000−2i2i0000000000i−i
χ4322-2-2-2-1222-122-2-2-2-211-1-121-211-1-12-2211-2-2-12-1-111-11-211-1-12-1-11100−2i2i2-2-1-122-1-1-1-111-2-2111100000000−2i2ii−iii−i−i0000−2i2i0000000000i−i
χ4422-2-2-2-1222-122-2-2-2-211-1-121-211-1-12-2211-2-2-12-1-111-11-211-1-12-1-11100−2i2i-2211-2-21111-1-122-1-1-1-100000000−2i2ii−iii−i−i00002i−2i0000000000−ii
χ45444444-2-244-2-2-2-2-2-244-2-214-2-2-2-2-21-2-2-2-2114-2-2-2-2-21-21111-2111114400000000000000000000-2-211-2-21100000000000000000000000000
χ46444444-2-244-2-2-2-2-2-244-2-214-2-2-2-2-21-2-2-2-2114-2-2-2-2-21-21111-211111-4-40000000000000000000022-1-122-1-100000000000000000000000000
χ4744444-24-24-24-2-2-244-2-2-21-2-2-211-21-24411-2-2-2-211-2-21-2-2111-2-21111000044-2-2-2-21111-2-2-2-211110000000000000000000000000000000000
χ4844444-24-24-24-2-2-244-2-2-21-2-2-211-21-24411-2-2-2-211-2-21-2-2111-2-211110000-4-42222-1-1-1-12222-1-1-1-10000000000000000000000000000000000
χ4944444-2-244-2-2444-2-2-2-21-2-2-24-2-21-2-2-2-2-2-2-2-2-24-2-21111-21111-21111004400000000000000000000000000-2-2-2-21111000000000000000000
χ5044444-2-244-2-2444-2-2-2-21-2-2-24-2-21-2-2-2-2-2-2-2-2-24-2-21111-21111-2111100-4-4000000000000000000000000002222-1-1-1-1000000000000000000
χ514444-444-2-444-2-2-244444-2-2-42224-2-2-4-4-2-2-2-2-422244-2-4222-2-4222-2-200000000000000000000000000000000000000000000000000000000
χ524444-44-24-44-2444-2-244-24-2-4-4-4-4-24-22244-2-2-4-4-4-4-2-2-22222-22222-2-200000000000000000000000000000000000000000000000000000000
χ534444-44-2-2-44-2-2-2-2-2-244-2-21-4222-2-2122-2-211-4222-2-212-1-1-112-1-1-1110000000000000000000000003-3003-300000000000000000000000000
χ544444-44-2-2-44-2-2-2-2-2-244-2-21-4222-2-2122-2-211-4222-2-212-1-1-112-1-1-111000000000000000000000000-3300-3300000000000000000000000000
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χ824-44i−4i0-24-202-42−2i2i4i−4i−2i2i-21-2003-32-1200i−i−2i2i003i−3i−2i2i1003-3-1003i−3ii−i0000006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000000000000000
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χ844-44i−4i0-24-202-42−2i2i4i−4i−2i2i-21-200-332-1200i−i−2i2i00−3i3i−2i2i100-33-100−3i3ii−i0000006−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000000000000000
χ854-44i−4i0-24-202-42−2i2i4i−4i−2i2i-21-200-332-1200i−i−2i2i00−3i3i−2i2i100-33-100−3i3ii−i000000−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000000000000000
χ864-4−4i4i04440-4-4-4−4i4i−4i4i−4i4i4440000-4-4-400−4i4i−4i4i0000−4i4i40000-40000−4i4i00000000000000000000000000000000000000000000000000000000
χ874-4−4i4i044-20-4-422i−2i−4i4i−4i4i4-2-20000-422002i−2i2i−2i0000−4i4i-20000200002i−2i00000000i6−i6i6−i6i6−i600−66−66−660000000000000000000000000000000000
χ884-4−4i4i044-20-4-422i−2i−4i4i−4i4i4-2-20000-422002i−2i2i−2i0000−4i4i-20000200002i−2i00000000−i6i6−i6i6−i6i6006−66−66−60000000000000000000000000000000000
χ894-4−4i4i04-240-42-4−4i4i2i−2i−4i4i-24-200002-4200−4i4i2i−2i00002i−2i-20000200002i−2i00000000000000000000000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000
χ904-4−4i4i04-240-42-4−4i4i2i−2i−4i4i-24-200002-4200−4i4i2i−2i00002i−2i-20000200002i−2i00000000000000000000000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000
χ914-4−4i4i0-24402-4-4−4i4i−4i4i2i−2i-2-24000022-4002i−2i−4i4i00002i−2i-20000200002i−2i0000006−6006−6−66−i6i600i6−i6−i6i60000000000000000000000000000000000
χ924-4−4i4i0-24402-4-4−4i4i−4i4i2i−2i-2-24000022-4002i−2i−4i4i00002i−2i-20000200002i−2i000000−6600−666−6i6−i600−i6i6i6−i60000000000000000000000000000000000
χ934-4−4i4i0-24-202-422i−2i−4i4i2i−2i-21-2003-32-1200−ii2i−2i00−3i3i2i−2i1003-3-100−3i3i−ii0000006−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000000000000000
χ944-4−4i4i0-24-202-422i−2i−4i4i2i−2i-21-2003-32-1200−ii2i−2i00−3i3i2i−2i1003-3-100−3i3i−ii000000−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000000000000000
χ954-4−4i4i0-24-202-422i−2i−4i4i2i−2i-21-200-332-1200−ii2i−2i003i−3i2i−2i100-33-1003i−3i−ii0000006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000000000000000
χ964-4−4i4i0-24-202-422i−2i−4i4i2i−2i-21-200-332-1200−ii2i−2i003i−3i2i−2i100-33-1003i−3i−ii000000−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000000000000000
χ9788888-4-4-48-4-4-4-4-4-4-4-4-4222-4-422222-4-42222-4-42222-122-1-1-122-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-8-4-4-4-8-4-4-4-4-4-4-4-4-422244-2-222244222244-2-222-1-2-211-1-2-211-1-100000000000000000000000000000000000000000000000000000000
χ9988-8-88-4-4-4-8-4-4-4444444222-4-422222-44-2-2-2-244-2-2-2-2-122-1-1-1-2-2111100000000000000000000000000000000000000000000000000000000
χ10088-8-8-8-4-4-48-4-4-444444422244-2-22224-4-2-2-2-2-4-422-2-2-1-2-211-122-1-11100000000000000000000000000000000000000000000000000000000
χ1018-88i−8i08-4-40-844−4i4i−4i4i8i−8i-4-42000044-200−4i4i2i−2i0000−4i4i20000-200002i−2i00000000000000000000000000000000000000000000000000000000
χ1028-88i−8i0-4-48044-88i−8i−4i4i−4i4i2-4-40000-24400−4i4i−4i4i00002i−2i20000-200002i−2i00000000000000000000000000000000000000000000000000000000
χ1038-88i−8i0-4-4-40444−4i4i−4i4i−4i4i222006-6-2-2-2002i−2i2i−2i006i−6i2i−2i-100-33100−3i3i−ii00000000000000000000000000000000000000000000000000000000
χ1048-88i−8i0-4-4-40444−4i4i−4i4i−4i4i22200-66-2-2-2002i−2i2i−2i00−6i6i2i−2i-1003-31003i−3i−ii00000000000000000000000000000000000000000000000000000000
χ1058-8−8i8i08-4-40-8444i−4i4i−4i−8i8i-4-42000044-2004i−4i−2i2i00004i−4i20000-20000−2i2i00000000000000000000000000000000000000000000000000000000
χ1068-8−8i8i0-4-48044-8−8i8i4i−4i4i−4i2-4-40000-244004i−4i4i−4i0000−2i2i20000-20000−2i2i00000000000000000000000000000000000000000000000000000000
χ1078-8−8i8i0-4-4-404444i−4i4i−4i4i−4i222006-6-2-2-200−2i2i−2i2i00−6i6i−2i2i-100-331003i−3ii−i00000000000000000000000000000000000000000000000000000000
χ1088-8−8i8i0-4-4-404444i−4i4i−4i4i−4i22200-66-2-2-200−2i2i−2i2i006i−6i−2i2i-1003-3100−3i3ii−i00000000000000000000000000000000000000000000000000000000

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