Finite Group Databasebeta

← Group #13155739

Character table — Group #13155739

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222244444444444444444488888888888888999912121212121212121212121212121818181818181818181818181818242424242424242424242424242424242424242436363636363636363636108108
order12442333466612121212121233366666612121212121212121236666661212121212121288882466888812122424242444448888882424242466612121224242424242424242424242424241212121224242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ511111111111111111111111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111
χ911-1-1-11111111-1-1-1-1-1-1111-1-1111-111-1-1-1-1-1-111-1-1-1-1-1111111-1-1ii−i−i1-111i−ii−i-1-1ii−i−iii−i−ii−i11-1-1ii−i−i111-1-1-1i−ii−ii−iii−i−iii−i−iii−i−ii−i11-1-11-1
χ1011-1-1-11111111-1-1-1-1-1-1111-1-1111-111-1-1-1-1-1-111-1-1-1-1-1111111-1-1ii−i−i1-111i−i−ii-1-1ii−i−i−i−iiii−i-1-111ii−i−i111-1-1-1−iii−i−iiii−i−i−i−iii−i−iiii−i-1-111-11
χ1111-1-1-11111111-1-1-1-1-1-1111-1-1111-111-1-1-1-1-1-111-1-1-1-1-1111111-1-1ii−i−i-11-1-1−iii−i11−i−iii−i−iiii−i-1-111ii−i−i-1-1-1111i−i−iii−i−i−iiiii−i−i−i−iiii−i-1-1111-1
χ1211-1-1-11111111-1-1-1-1-1-1111-1-1111-111-1-1-1-1-1-111-1-1-1-1-1111111-1-1ii−i−i-11-1-1−ii−ii11−i−iiiii−i−ii−i11-1-1ii−i−i-1-1-1111−ii−ii−ii−i−iii−i−iiiii−i−ii−i11-1-1-11
χ1311-1-1-11111111-1-1-1-1-1-1111-1-1111-111-1-1-1-1-1-111-1-1-1-1-1111111-1-1−i−iii1-111−iii−i-1-1−i−iiiii−i−i−ii-1-111−i−iii111-1-1-1i−i−iii−i−i−iiiii−i−iii−i−i−ii-1-111-11
χ1411-1-1-11111111-1-1-1-1-1-1111-1-1111-111-1-1-1-1-1-111-1-1-1-1-1111111-1-1−i−iii1-111−ii−ii-1-1−i−iii−i−iii−ii11-1-1−i−iii111-1-1-1−ii−ii−ii−i−iii−i−iii−i−iii−ii11-1-11-1
χ1511-1-1-11111111-1-1-1-1-1-1111-1-1111-111-1-1-1-1-1-111-1-1-1-1-1111111-1-1−i−iii-11-1-1i−ii−i11ii−i−i−i−iii−ii11-1-1−i−iii-1-1-1111i−ii−ii−iii−i−iii−i−i−i−iii−ii11-1-1-11
χ1611-1-1-11111111-1-1-1-1-1-1111-1-1111-111-1-1-1-1-1-111-1-1-1-1-1111111-1-1−i−iii-11-1-1i−i−ii11ii−i−iii−i−i−ii-1-111−i−iii-1-1-1111−iii−i−iiii−i−i−i−iiiii−i−i−ii-1-1111-1
χ172222222-1222-12222-1-12-1-12-12-1-122-1-1-122-1-12-12-1-1-1-1-12-1-1-1-1-1-1222222-1-12200-1-1-1-1-1-10000220000-1-1-1-12-1-12-1-1002200-1-1-1-100000000-1-1000000
χ182222222-1222-12222-1-12-1-12-12-1-122-1-1-122-1-12-12-1-1-1-1-12-1-1-1-1-1-12222-2-211-2-2001111110000220000-1-1-1-1-211-21100-2-200111100000000-1-1000000
χ192222222-1222-12222-1-12-1-12-12-1-122-1-1-122-1-12-12-1-1-1-1-12-1-1-1-1-1-1-2-2-2-222-1-1-2-200-1-111110000-2-2000011112-1-12-1-100-2-20011110000000011000000
χ202222222-1222-12222-1-12-1-12-12-1-122-1-1-122-1-12-12-1-1-1-1-12-1-1-1-1-1-1-2-2-2-2-2-211220011-1-1-1-10000-2-200001111-211-211002200-1-1-1-10000000011000000
χ21222222-1222-12-1-12222-12-122-12-1-1-12-1-1-1-1222-1-12-1-1-1-1-12-1-1-1-1-100002222002222000022220000000000-1-1-1-1-1-1-1-100220000-1-1-1-1-1-1-1-100000000
χ22222222-1222-12-1-12222-12-122-12-1-1-12-1-1-1-1222-1-12-1-1-1-1-12-1-1-1-1-10000222200-2-2220000-2-2-2-20000000000-1-1-1-1-1-11100-2-200001111111100000000
χ23222222-1222-12-1-12222-12-122-12-1-1-12-1-1-1-1222-1-12-1-1-1-1-12-1-1-1-1-10000-2-2-2-20022-2-20000-2-2-2-20000000000111111-1-100220000-1-1-1-1111100000000
χ24222222-1222-12-1-12222-12-122-12-1-1-12-1-1-1-1222-1-12-1-1-1-1-12-1-1-1-1-10000-2-2-2-200-2-2-2-20000222200000000001111111100-2-200001111-1-1-1-100000000
χ2522222-1222-12222-1-122-1-12-12-1-1222222-1-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-10000000022220022220000002222000000000022-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-100
χ2622222-1222-12222-1-122-1-12-12-1-1222222-1-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-10000000022-2-2002222000000-2-2-2-20000000000-2-2-1-111-1-1-1-11111000000111100
χ2722222-1222-12222-1-122-1-12-12-1-1222222-1-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-100000000-2-22200-2-2-2-2000000-2-2-2-200000000002211-1-11111-1-1-1-1000000111100
χ2822222-1222-12222-1-122-1-12-12-1-1222222-1-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-100000000-2-2-2-200-2-2-2-200000022220000000000-2-2111111111111000000-1-1-1-100
χ292222-2222-2222222222222-2-2222-2-2-2222222-22-2-2-2-2-22-2-2-2-2-2222222000000000000000000-2-200002222000000000000000000000000-2-2000000
χ302222-2222-2222222222222-2-2222-2-2-2222222-22-2-2-2-2-22-2-2-2-2-222-2-2-2-2000000000000000000220000-2-2-2-200000000000000000000000022000000
χ312222-222-1-222-12222-1-12-1-1-212-1-1-2-21-1-122-1-1-2-1-21111-1-21111-1-1222200−i3i30000−i3i3−i3i3−i3i30000-2-20000-1-1-1-10−i3i30−i3i3000000−i3i3−i3i30000000011000000
χ322222-222-1-222-12222-1-12-1-1-212-1-1-2-21-1-122-1-1-2-1-21111-1-21111-1-1222200i3−i30000i3−i3i3−i3i3−i30000-2-20000-1-1-1-10i3−i30i3−i3000000i3−i3i3−i30000000011000000
χ332222-222-1-222-12222-1-12-1-1-212-1-1-2-21-1-122-1-1-2-1-21111-1-21111-1-1-2-2-2-200−i3i30000−i3i3i3−i3i3−i3000022000011110−i3i30−i3i3000000i3−i3i3−i300000000-1-1000000
χ342222-222-1-222-12222-1-12-1-1-212-1-1-2-21-1-122-1-1-2-1-21111-1-21111-1-1-2-2-2-200i3−i30000i3−i3−i3i3−i3i3000022000011110i3−i30i3−i3000000−i3i3−i3i300000000-1-1000000
χ3522-2-22222-2222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-22i2i−2i−2i000000000000000000−2i2i00002i2i−2i−2i000000000000000000000000−2i2i000000
χ3622-2-22222-2222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2−2i−2i2i2i0000000000000000002i−2i0000−2i−2i2i2i0000000000000000000000002i−2i000000
χ3722-2-2222-1-222-1-2-2-2-2112-1-12-12-1-12-2111-2-211-2-12-1-1-1-1-1-21111112i2i−2i−2i00−i3i30000i3−i33−3−330000−2i2i0000−i−iii0−i3i30i3−i30000003−3−3300000000i−i000000
χ3822-2-2222-1-222-1-2-2-2-2112-1-12-12-1-12-2111-2-211-2-12-1-1-1-1-1-21111112i2i−2i−2i00i3−i30000−i3i3−333−30000−2i2i0000−i−iii0i3−i30−i3i3000000−333−300000000i−i000000
χ3922-2-2222-1-222-1-2-2-2-2112-1-12-12-1-12-2111-2-211-2-12-1-1-1-1-1-2111111−2i−2i2i2i00−i3i30000i3−i3−333−300002i−2i0000ii−i−i0−i3i30i3−i3000000−333−300000000−ii000000
χ4022-2-2222-1-222-1-2-2-2-2112-1-12-12-1-12-2111-2-211-2-12-1-1-1-1-1-2111111−2i−2i2i2i00i3−i30000−i3i33−3−3300002i−2i0000ii−i−i0i3−i30−i3i30000003−3−3300000000−ii000000
χ4122-2-2-222-1222-1-2-2-2-2112-1-1-212-1-1-22-111-2-2112-1-21111-12-1-1-1-1112i2i−2i−2i2-2-1-12i−2i0011−i−iii00002i−2i0000−i−iii2-1-1-211002i−2i00−i−iii00000000−ii000000
χ4222-2-2-222-1222-1-2-2-2-2112-1-1-212-1-1-22-111-2-2112-1-21111-12-1-1-1-1112i2i−2i−2i-2211−2i2i00-1-1ii−i−i00002i−2i0000−i−iii-2112-1-100−2i2i00ii−i−i00000000−ii000000
χ4322-2-2-222-1222-1-2-2-2-2112-1-1-212-1-1-22-111-2-2112-1-21111-12-1-1-1-111−2i−2i2i2i2-2-1-1−2i2i0011ii−i−i0000−2i2i0000ii−i−i2-1-1-21100−2i2i00ii−i−i00000000i−i000000
χ4422-2-2-222-1222-1-2-2-2-2112-1-1-212-1-1-22-111-2-2112-1-21111-12-1-1-1-111−2i−2i2i2i-22112i−2i00-1-1−i−iii0000−2i2i0000ii−i−i-2112-1-1002i−2i00−i−iii00000000i−i000000
χ4522-2-2-22-1222-1211-2-2-2-2-12-1-2-2-12-11-121111-2-22-11-2111-1-12-1-1-11100002-222002i−2i-2-200002i2i−2i−2i0000000000-1-1-1111−ii002i−2i0000−i−iii−i−iii00000000
χ4622-2-2-22-1222-1211-2-2-2-2-12-1-2-2-12-11-121111-2-22-11-2111-1-12-1-1-11100002-22200−2i2i-2-20000−2i−2i2i2i0000000000-1-1-1111i−i00−2i2i0000ii−i−iii−i−i00000000
χ4722-2-2-22-1222-1211-2-2-2-2-12-1-2-2-12-11-121111-2-22-11-2111-1-12-1-1-1110000-22-2-2002i−2i220000−2i−2i2i2i0000000000111-1-1-1−ii002i−2i0000−i−iiiii−i−i00000000
χ4822-2-2-22-1222-1211-2-2-2-2-12-1-2-2-12-11-121111-2-22-11-2111-1-12-1-1-1110000-22-2-200−2i2i2200002i2i−2i−2i0000000000111-1-1-1i−i00−2i2i0000ii−i−i−i−iii00000000
χ4922-2-2-2-1222-122-2-211-2-2-1-121-2-1-12-222-2-21111-1-111-211-1-1-12-1-111000000002i−2i2i−2i002i2i−2i−2i00000022-2-200000000002i−2i−ii−ii−i−iii−i−iii000000-1-11100
χ5022-2-2-2-1222-122-2-211-2-2-1-121-2-1-12-222-2-21111-1-111-211-1-1-12-1-111000000002i−2i−2i2i002i2i−2i−2i000000-2-2220000000000−2i2i−iii−i−i−iiiii−i−i00000011-1-100
χ5122-2-2-2-1222-122-2-211-2-2-1-121-2-1-12-222-2-21111-1-111-211-1-1-12-1-11100000000−2i2i2i−2i00−2i−2i2i2i000000-2-22200000000002i−2ii−i−iiii−i−i−i−iii00000011-1-100
χ5222-2-2-2-1222-122-2-211-2-2-1-121-2-1-12-222-2-21111-1-111-211-1-1-12-1-11100000000−2i2i−2i2i00−2i−2i2i2i00000022-2-20000000000−2i2ii−ii−iii−i−iii−i−i000000-1-11100
χ532-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200-2-2-20002i−2i2i−2i2i−2i0200000-2000002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000001+i−1−i1−i−1+i002−2−i2i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000001+i−1−i1−i−1+i002−2−i2i200
χ542-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200-2-2-20002i−2i2i−2i2i−2i0200000-2000002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000−1−i1+i−1+i1−i00−22i2−i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000−1−i1+i−1+i1−i00−22i2−i200
χ552-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200-2-2-20002i−2i2i−2i2i−2i0200000-2000002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000001+i−1−i1−i−1+i00−22i2−i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000001+i−1−i1−i−1+i00−22i2−i200
χ562-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200-2-2-20002i−2i2i−2i2i−2i0200000-2000002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000−1−i1+i−1+i1−i002−2−i2i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000−1−i1+i−1+i1−i002−2−i2i200
χ572-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i22200-2-2-2000−2i2i−2i2i−2i2i0200000-200000−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000001−i−1+i1+i−1−i002−2i2−i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000001−i−1+i1+i−1−i002−2i2−i200
χ582-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i22200-2-2-2000−2i2i−2i2i−2i2i0200000-200000−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000−1+i1−i−1−i1+i00−22−i2i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000−1+i1−i−1−i1+i00−22−i2i200
χ592-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i22200-2-2-2000−2i2i−2i2i−2i2i0200000-200000−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000001−i−1+i1+i−1−i00−22−i2i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000001−i−1+i1+i−1−i00−22−i2i200
χ602-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i22200-2-2-2000−2i2i−2i2i−2i2i0200000-200000−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000−1+i1−i−1−i1+i002−2i2−i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000−1+i1−i−1−i1+i002−2i2−i200
χ61444444-2-244-2-2-2-244-2-2-2-214-2-2-21-2-2-211-2-2-2-241-2-21111-2-211111000044-2-20000-2-2000000000000000000-211-21100000000000000000000000000
χ62444444-2-244-2-2-2-244-2-2-2-214-2-2-21-2-2-211-2-2-2-241-2-21111-2-2111110000-4-4220000220000000000000000002-1-12-1-100000000000000000000000000
χ6344444-24-24-24-244-2-2-2-2-21-2-2-2-21-244-2-2-2-2-211-21-21-2111-21-2111100000000440000-2-2-2-20000000000000000000000-2-20011110000000000000000
χ6444444-24-24-24-244-2-2-2-2-21-2-2-2-21-244-2-2-2-2-211-21-21-2111-21-2111100000000-4-40000222200000000000000000000002200-1-1-1-10000000000000000
χ6544444-2-244-2-24-2-2-2-2441-2-2-241-2-2-2-24-2-211-2-2-211-2-21111-2-2111100000000004400000000000000000000000000-2-200-2-200001111000000000000
χ6644444-2-244-2-24-2-2-2-2441-2-2-241-2-2-2-24-2-211-2-2-211-2-21111-2-211110000000000-4-4000000000000000000000000002200220000-1-1-1-1000000000000
χ674444-44-24-44-24-2-24444-24-2-4-4-24-222-4-2-2-2-244-4-22-4222-22-4222-2-20000000000000000000000000000000000000000000000000000000000000000
χ684444-44-2-2-44-2-2-2-244-2-2-2-21-42-2-2122211-2-2-2-2-4122-1-1-1122-1-1-111000000−2i32i30000−2i32i30000000000000000000i3−i30i3−i300000000000000000000000000
χ694444-44-2-2-44-2-2-2-244-2-2-2-21-42-2-2122211-2-2-2-2-4122-1-1-1122-1-1-1110000002i3−2i300002i3−2i30000000000000000000−i3i30−i3i300000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.