Finite Group Databasebeta

← Group #10801650

Character table — Group #10801650

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11111111222222222222444444444444444444444444666666668888888888888888888888881212121212121212121212121212121216161616242424242424
order12224444223446661212121222444444668888888812122424242488888888246688881212121212122424242424242424242444444444888888886122424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ5111111111111111111111111-1-1-1-1111111111111111111111111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-111-1-1-1-1
χ911111111111111111111-1-1-1-11111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111
χ1211111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-111-1-1-1-111
χ171111-1-1-1-1-1-1111111-1-1-1-111-1-1ii−i−i-1-1ii−i−iii−i−i11ii−i−iiiii−i−i−i−i1-111i−i1-1-1-1ii−i−ii−iii−i−i11-1-111-1-111-1-1ii−i−i11-1-11-1i−i1-1i−ii−i
χ181111-1-1-1-1-1-1111111-1-1-1-111-1-1ii−i−i-1-1ii−i−iii−i−i11ii−i−i−i−i−i−iiiii1-111i−i1-1-1-1ii−i−ii−iii−i−i11-1-1-1-111-1-111−i−iii-1-1111-1i−i-11−ii−ii
χ191111-1-1-1-1-1-1111111-1-1-1-111-1-1ii−i−i-1-1−i−iii−i−iii11−i−iiiiiii−i−i−i−i-1111i−i-11-1-1ii−i−i−ii−i−iii-1-111-1-111-1-111ii−i−i11-1-1-11i−i1-1−ii−ii
χ201111-1-1-1-1-1-1111111-1-1-1-111-1-1ii−i−i-1-1−i−iii−i−iii11−i−iii−i−i−i−iiiii-1111i−i-11-1-1ii−i−i−ii−i−iii-1-11111-1-111-1-1−i−iii-1-111-11i−i-11i−ii−i
χ211111-1-1-1-1-1-1111111-1-1-1-111-1-1−i−iii-1-1ii−i−iii−i−i11ii−i−iiiii−i−i−i−i-1111−ii-11-1-1−i−iiii−iii−i−i-1-11111-1-111-1-1ii−i−i-1-111-11−ii-11−ii−ii
χ221111-1-1-1-1-1-1111111-1-1-1-111-1-1−i−iii-1-1ii−i−iii−i−i11ii−i−i−i−i−i−iiiii-1111−ii-11-1-1−i−iiii−iii−i−i-1-111-1-111-1-111−i−iii11-1-1-11−ii1-1i−ii−i
χ231111-1-1-1-1-1-1111111-1-1-1-111-1-1−i−iii-1-1−i−iii−i−iii11−i−iiiiiii−i−i−i−i1-111−ii1-1-1-1−i−iii−ii−i−iii11-1-1-1-111-1-111ii−i−i-1-1111-1−ii-11i−ii−i
χ241111-1-1-1-1-1-1111111-1-1-1-111-1-1−i−iii-1-1−i−iii−i−iii11−i−iii−i−i−i−iiiii1-111−ii1-1-1-1−i−iii−ii−i−iii11-1-111-1-111-1-1−i−iii11-1-11-1−ii1-1−ii−ii
χ251111-1-1-1-1-1-1111111-1-1-1-1-1-111ii−i−i-1-1ii−i−i−i−iii11ii−i−iiiii−i−i−i−i-11-1-1−ii1-111ii−i−ii−i−i−iii11-1-111-1-1-1-111−i−iii11-1-1-11−ii-11i−i−ii
χ261111-1-1-1-1-1-1111111-1-1-1-1-1-111ii−i−i-1-1ii−i−i−i−iii11ii−i−i−i−i−i−iiiii-11-1-1−ii1-111ii−i−ii−i−i−iii11-1-1-1-11111-1-1ii−i−i-1-111-11−ii1-1−iii−i
χ271111-1-1-1-1-1-1111111-1-1-1-1-1-111ii−i−i-1-1−i−iiiii−i−i11−i−iiiiiii−i−i−i−i1-1-1-1−ii-1111ii−i−i−iiii−i−i-1-111-1-11111-1-1−i−iii11-1-11-1−ii-11−iii−i
χ281111-1-1-1-1-1-1111111-1-1-1-1-1-111ii−i−i-1-1−i−iiiii−i−i11−i−iii−i−i−i−iiiii1-1-1-1−ii-1111ii−i−i−iiii−i−i-1-11111-1-1-1-111ii−i−i-1-1111-1−ii1-1i−i−ii
χ291111-1-1-1-1-1-1111111-1-1-1-1-1-111−i−iii-1-1ii−i−i−i−iii11ii−i−iiiii−i−i−i−i1-1-1-1i−i-1111−i−iiii−i−i−iii-1-11111-1-1-1-111−i−iii-1-1111-1i−i1-1−iii−i
χ301111-1-1-1-1-1-1111111-1-1-1-1-1-111−i−iii-1-1ii−i−i−i−iii11ii−i−i−i−i−i−iiiii1-1-1-1i−i-1111−i−iiii−i−i−iii-1-111-1-11111-1-1ii−i−i11-1-11-1i−i-11i−i−ii
χ311111-1-1-1-1-1-1111111-1-1-1-1-1-111−i−iii-1-1−i−iiiii−i−i11−i−iiiiiii−i−i−i−i-11-1-1i−i1-111−i−iii−iiii−i−i11-1-1-1-11111-1-1−i−iii-1-111-11i−i1-1i−i−ii
χ321111-1-1-1-1-1-1111111-1-1-1-1-1-111−i−iii-1-1−i−iiiii−i−i11−i−iii−i−i−i−iiiii-11-1-1i−i1-111−i−iii−iiii−i−i11-1-111-1-1-1-111ii−i−i11-1-1-11i−i-11−iii−i
χ332222222222-122-1-1-1-1-1-1-122222222-1-122222222-1-1-1-1-1-10000000022-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ342222222222-122-1-1-1-1-1-1-122222222-1-1-2-2-2-2-2-2-2-2-1-1111100000000-2-2-1-122-2-2-1-1-1-1-1-11111111111000000000000000011-1-1000000
χ352222222222-122-1-1-1-1-1-1-12222-2-2-2-2-1-122222222-1-1-1-1-1-100000000-2-2-1-1-2-2-2-2-1-11111-1-1-1-1-1-1111100000000000000001111000000
χ362222222222-122-1-1-1-1-1-1-12222-2-2-2-2-1-1-2-2-2-2-2-2-2-2-1-111110000000022-1-1-2-222-1-11111111111-1-1-1-10000000000000000-1-111000000
χ372222222222-122-1-1-1-1-1-1-1-2-2-2-22222-1-12222-2-2-2-2-1-1-1-1-1-100000000-2-211-2-22211-1-1-1-1-1-11111-1-1-1-100000000000000001111000000
χ382222222222-122-1-1-1-1-1-1-1-2-2-2-22222-1-1-2-2-2-22222-1-11111000000002211-2-2-2-211-1-1-1-111-1-1-1-111110000000000000000-1-111000000
χ392222222222-122-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-12222-2-2-2-2-1-1-1-1-1-100000000221122-2-2111111-1-1111111110000000000000000-1-1-1-1000000
χ402222222222-122-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-2-2-2-22222-1-1111100000000-2-211222211111111-1-1-1-1-1-1-1-1000000000000000011-1-1000000
χ4122222222-2-22-2-2222222200000000-2-22-22-20000-2-2222222-2-222-2-200000000000000-2-2000000002-22-20000000000000000000000
χ4222222222-2-22-2-2222222200000000-2-22-22-20000-2-22222-2-222-2-22200000000000000-2-200000000-22-220000000000000000000000
χ4322222222-2-22-2-2222222200000000-2-2-22-220000-2-2-2-2-2-222-2-222-2-2000000000000002200000000-22-220000000000000000000000
χ4422222222-2-22-2-2222222200000000-2-2-22-220000-2-2-2-2-2-2-2-222-2-2220000000000000022000000002-22-20000000000000000000000
χ452222-2-2-2-2222-2-2222-2-2-2-200000000222i−2i−2i2i0000-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000−2i2i000000002-2-220000000000000000000000
χ462222-2-2-2-2222-2-2222-2-2-2-200000000222i−2i−2i2i0000-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000−2i2i00000000-222-20000000000000000000000
χ472222-2-2-2-2222-2-2222-2-2-2-20000000022−2i2i2i−2i0000-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000002i−2i00000000-222-20000000000000000000000
χ482222-2-2-2-2222-2-2222-2-2-2-20000000022−2i2i2i−2i0000-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000002i−2i000000002-2-220000000000000000000000
χ492222-2-2-2-2-2-2-122-1-1-1111122-2-22i2i−2i−2i112i2i−2i−2i2i2i−2i−2i-1-1−i−iii000000002-2-1-12i−2i2-211−i−iii−ii−i−iii-1-1110000000000000000-11−ii000000
χ502222-2-2-2-2-2-2-122-1-1-1111122-2-22i2i−2i−2i11−2i−2i2i2i−2i−2i2i2i-1-1ii−i−i00000000-22-1-12i−2i-2211−i−iiii−iii−i−i11-1-100000000000000001-1−ii000000
χ512222-2-2-2-2-2-2-122-1-1-1111122-2-2−2i−2i2i2i112i2i−2i−2i2i2i−2i−2i-1-1−i−iii00000000-22-1-1−2i2i-2211ii−i−i−ii−i−iii11-1-100000000000000001-1i−i000000
χ522222-2-2-2-2-2-2-122-1-1-1111122-2-2−2i−2i2i2i11−2i−2i2i2i−2i−2i2i2i-1-1ii−i−i000000002-2-1-1−2i2i2-211ii−i−ii−iii−i−i-1-1110000000000000000-11i−i000000
χ532222-2-2-2-2-2-2-122-1-1-11111-2-2222i2i−2i−2i112i2i−2i−2i−2i−2i2i2i-1-1−i−iii00000000-2211−2i2i2-2-1-1−i−iii−iiii−i−i-1-11100000000000000001-1i−i000000
χ542222-2-2-2-2-2-2-122-1-1-11111-2-2222i2i−2i−2i11−2i−2i2i2i2i2i−2i−2i-1-1ii−i−i000000002-211−2i2i-22-1-1−i−iiii−i−i−iii11-1-10000000000000000-11i−i000000
χ552222-2-2-2-2-2-2-122-1-1-11111-2-222−2i−2i2i2i112i2i−2i−2i−2i−2i2i2i-1-1−i−iii000000002-2112i−2i-22-1-1ii−i−i−iiii−i−i11-1-10000000000000000-11−ii000000
χ562222-2-2-2-2-2-2-122-1-1-11111-2-222−2i−2i2i2i11−2i−2i2i2i2i2i−2i−2i-1-1ii−i−i00000000-22112i−2i2-2-1-1ii−i−ii−i−i−iii-1-11100000000000000001-1−ii000000
χ5722-2-222-2-22-22-22-2-22-2-2222-22-200002-200000000-2200002i−2i2i−2i2i−2i2i−2i002-200002-200000000000000000000002i−2i2i−2i00000000000000
χ5822-2-222-2-22-22-22-2-22-2-2222-22-200002-200000000-220000−2i2i−2i2i−2i2i−2i2i002-200002-20000000000000000000000−2i2i−2i2i00000000000000
χ5922-2-222-2-22-22-22-2-22-2-222-22-2200002-200000000-2200002i−2i2i−2i2i−2i2i−2i00-220000-220000000000000000000000−2i2i−2i2i00000000000000
χ6022-2-222-2-22-22-22-2-22-2-222-22-2200002-200000000-220000−2i2i−2i2i−2i2i−2i2i00-220000-2200000000000000000000002i−2i2i−2i00000000000000
χ6122-2-222-2-2-2222-2-2-22-2-22200000000-2200002-22-22-200002i−2i−2i2i2i−2i−2i2i00000000000000002-22-2000000002i−2i2i−2i000000000000000000
χ6222-2-222-2-2-2222-2-2-22-2-22200000000-2200002-22-22-20000−2i2i2i−2i−2i2i2i−2i00000000000000002-22-200000000−2i2i−2i2i000000000000000000
χ6322-2-222-2-2-2222-2-2-22-2-22200000000-220000-22-222-200002i−2i−2i2i2i−2i−2i2i0000000000000000-22-2200000000−2i2i−2i2i000000000000000000
χ6422-2-222-2-2-2222-2-2-22-2-22200000000-220000-22-222-20000−2i2i2i−2i−2i2i2i−2i0000000000000000-22-22000000002i−2i2i−2i000000000000000000
χ6522-2-2-2-2222-222-2-2-2222-2-2000000002-200002i−2i−2i2i2-200002-2-22-222-200000000000000002i−2i−2i2i00000000−2i2i2i−2i000000000000000000
χ6622-2-2-2-2222-222-2-2-2222-2-2000000002-200002i−2i−2i2i2-20000-222-22-2-2200000000000000002i−2i−2i2i000000002i−2i−2i2i000000000000000000
χ6722-2-2-2-2222-222-2-2-2222-2-2000000002-20000−2i2i2i−2i2-200002-2-22-222-20000000000000000−2i2i2i−2i000000002i−2i−2i2i000000000000000000
χ6822-2-2-2-2222-222-2-2-2222-2-2000000002-20000−2i2i2i−2i2-20000-222-22-2-220000000000000000−2i2i2i−2i00000000−2i2i2i−2i000000000000000000
χ6922-2-2-2-222-222-22-2-2222-2-22-2-220000-2200000000-2200002-22-2-22-22002-20000-2200000000000000000000002-2-2200000000000000
χ7022-2-2-2-222-222-22-2-2222-2-22-2-220000-2200000000-220000-22-222-22-2002-20000-220000000000000000000000-222-200000000000000
χ7122-2-2-2-222-222-22-2-2222-2-2-222-20000-2200000000-2200002-22-2-22-2200-2200002-20000000000000000000000-222-200000000000000
χ7222-2-2-2-222-222-22-2-2222-2-2-222-20000-2200000000-220000-22-222-22-200-2200002-200000000000000000000002-2-2200000000000000
χ7344444444-4-4-2-4-4-2-2-2-2-2-2-200000000224-44-4000022-2-2-2-20000000000000000000000220000000000000000000000000000000000
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χ7944-4-444-4-4-44-24-422-222-2-2000000002-200004-44-4-220000000000000000000000000000-22-22000000000000000000000000000000
χ8044-4-444-4-4-44-24-422-222-2-2000000002-20000-44-44-2200000000000000000000000000002-22-2000000000000000000000000000000
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χ8244-4-4-4-4444-4-24-422-2-2-22200000000-220000−4i4i4i−4i-2200000000000000000000000000002i−2i−2i2i000000000000000000000000000000
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χ874-44-4−4i4i−4i4i004004-4-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000022−222i2−2i20000000000
χ884-44-4−4i4i−4i4i004004-4-4−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000−2222−2i22i20000000000
χ894-4-444i−4i−4i4i00400-44-4−4i4i4i−4i00002+2i−2−2i2−2i−2+2i00000000000000000000000000000000002+2i−2−2i2−2i−2+2i000000000000000000000000000000000000
χ904-4-444i−4i−4i4i00400-44-4−4i4i4i−4i0000−2−2i2+2i−2+2i2−2i0000000000000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000
χ914-4-444i−4i−4i4i00-2002-222i−2i−2i2i00002+2i−2−2i2−2i−2+2i000000000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000000000000000000−1−i1+i−1+i1−i000000i6−i66−600000000000000000000000000
χ924-4-444i−4i−4i4i00-2002-222i−2i−2i2i00002+2i−2−2i2−2i−2+2i0000000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000000000000000000−1−i1+i−1+i1−i000000−i6i6−6600000000000000000000000000
χ934-4-444i−4i−4i4i00-2002-222i−2i−2i2i0000−2−2i2+2i−2+2i2−2i000000000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ130000000000000000001+i−1−i1−i−1+i000000−i6i6−6600000000000000000000000000
χ944-4-444i−4i−4i4i00-2002-222i−2i−2i2i0000−2−2i2+2i−2+2i2−2i0000000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ130000000000000000001+i−1−i1−i−1+i000000i6−i66−600000000000000000000000000
χ954-4-44−4i4i4i−4i00400-44-44i−4i−4i4i00002−2i−2+2i2+2i−2−2i00000000000000000000000000000000002−2i−2+2i2+2i−2−2i000000000000000000000000000000000000
χ964-4-44−4i4i4i−4i00400-44-44i−4i−4i4i0000−2+2i2−2i−2−2i2+2i0000000000000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000
χ974-4-44−4i4i4i−4i00-2002-22−2i2i2i−2i00002−2i−2+2i2+2i−2−2i0000000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000000000000000000−1+i1−i−1−i1+i000000−i6i66−600000000000000000000000000
χ984-4-44−4i4i4i−4i00-2002-22−2i2i2i−2i00002−2i−2+2i2+2i−2−2i000000000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000000000000000000−1+i1−i−1−i1+i000000i6−i6−6600000000000000000000000000
χ994-4-44−4i4i4i−4i00-2002-22−2i2i2i−2i0000−2+2i2−2i−2−2i2+2i0000000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ230000000000000000001−i−1+i1+i−1−i000000i6−i6−6600000000000000000000000000
χ1004-4-44−4i4i4i−4i00-2002-22−2i2i2i−2i0000−2+2i2−2i−2−2i2+2i000000000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ230000000000000000001−i−1+i1+i−1−i000000−i6i66−600000000000000000000000000
χ1018-88-88i−8i8i−8i00-400-444−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8−8i8i−8i8i00-400-4444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000000000

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