Finite Group Databasebeta

← Group #72342844

Character table — Group #72342844

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size112222233444444444666668888881212121212121212121616161616161616161616161616242432323232323232323232484848484848484848484848484848484848484864646464646464649696969696969696
order1224488224488816161616244883666161644888161616162244121212121212242424241616242448484848484848482244323232323232323232323232323232326666121212121616161616161616
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111-1-11-1-1-1-1-1-111111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ6111111111-1-11-1-1-1-1-1-111111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ7111111111-1-11-1-1-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ8111111111-1-11-1-1-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ911-11-1-1-111i−i1i−iii−i−i-11-1-1-111-1-11-1i−i1i−iii−i−i1-1i−iii−i−i1-111-1-11-1i−i11-1-1ii−i−i1-1i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1311-1-1ii−i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1011-11-1-1-111i−i1i−iii−i−i-11-1-1-111-1-11-1i−i1i−iii−i−i1-1i−iii−i−i1-111-1-11-1i−i11-1-1ii−i−i1-1i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1311-1-1ii−i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1111-11-1-1-111i−i1i−iii−i−i-11-1-1-111-1-11-1i−i1i−iii−i−i-11−iiii−i−i1-111-1-11-1i−i11-1-1ii−i−i-11−iiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13-1-111−i−iii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ1211-11-1-1-111i−i1i−iii−i−i-11-1-1-111-1-11-1i−i1i−iii−i−i-11−iiii−i−i1-111-1-11-1i−i11-1-1ii−i−i-11−ii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13-1-111−i−iiiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ1311-11-1-1-111−ii1−ii−i−iii-11-1-1-111-1-11-1−ii1−ii−i−iii1-1−ii−i−iii1-111-1-11-1−ii11-1-1−i−iii1-1−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2311-1-1−i−iii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1411-11-1-1-111−ii1−ii−i−iii-11-1-1-111-1-11-1−ii1−ii−i−iii1-1−ii−i−iii1-111-1-11-1−ii11-1-1−i−iii1-1−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2311-1-1−i−iiiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1511-11-1-1-111−ii1−ii−i−iii-11-1-1-111-1-11-1−ii1−ii−i−iii-11i−i−i−iii1-111-1-11-1−ii11-1-1−i−iii-11i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23-1-111ii−i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ1611-11-1-1-111−ii1−ii−i−iii-11-1-1-111-1-11-1−ii1−ii−i−iii-11i−i−i−iii1-111-1-11-1−ii11-1-1−i−iii-11i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23-1-111ii−i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ1722222222222222222222222-1-1-1-1222222222222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122220000000000000000-1-1-1-1-1-1-1-100000000
χ1822222222222222222222222-1-1-1-122222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000000000001111111100000000
χ1922222222222222-2-2-2-2222222222-2-222222-2-2-2-200002222222222-2-222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ2022222222222222-2-2-2-222222-1-1-1-1-2-222222-2-2-2-20000-1-1-1-1-1-1-1-1-1-1-2-2-1-11111111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ2122222222222222-2-2-2-222222-1-1-1-1-2-222222-2-2-2-20000-1-1-1-1-1-1-1-1-1-1-2-2-1-11111111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ22222222222-2-22-2-22222222222222-2-2-2-22-2-222220000-2-2-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ23222222222-2-22-2-2222222222-1-1-1-1-2-2-2-22-2-2222200001111-1-1-1-1-1-1-2-2111111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ24222222222-2-22-2-2222222222-1-1-1-1-2-2-2-22-2-2222200001111-1-1-1-1-1-1-2-2111111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ25222222222-2-22-2-2-2-2-2-222222-1-1-1-122-2-22-2-2-2-2-2-222-2-21111-1-1-1-1-1-12211-1-1-1-1111122-2-20000000000000000-1-1-1-1111100000000
χ26222222222-2-22-2-2-2-2-2-222222-1-1-1-122-2-22-2-2-2-2-2-2-2-2221111-1-1-1-1-1-12211-1-1-1-11111-2-22200000000000000001111-1-1-1-100000000
χ2722222-2-22222-2-2-20000222-2-222220022-2-2-200000000222222-2-2-2-200-2-2000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ2822222-2-22222-2-2-20000222-2-222220022-2-2-200000000222222-2-2-2-200-2-2000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ2922222-2-222-2-2-2220000222-2-2222200-2-2-22200000000-2-2-2-222-2-2-2-200220000000000002−22−2−22−222−22−2−22−220000000000000000
χ3022222-2-222-2-2-2220000222-2-2222200-2-2-22200000000-2-2-2-222-2-2-2-20022000000000000−22−222−22−2−22−222−22−20000000000000000
χ3122-22-222222i−2i-2−2i2i0000-22-22222-2-2002i−2i-2−2i2i000000002i2i−2i−2i2-2-2-22200−2i2i0000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ3222-22-222222i−2i-2−2i2i0000-22-22222-2-2002i−2i-2−2i2i000000002i2i−2i−2i2-2-2-22200−2i2i000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ3322-22-22222−2i2i-22i−2i0000-22-22222-2-200−2i2i-22i−2i00000000−2i−2i2i2i2-2-2-222002i−2i0000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ3422-22-22222−2i2i-22i−2i0000-22-22222-2-200−2i2i-22i−2i00000000−2i−2i2i2i2-2-2-222002i−2i000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ3522-22-2-2-2222i−2i22i−2i2i2i−2i−2i-22-2-2-2-1-1112-22i−2i22i−2i2i2i−2i−2i2-22i−2i−i−iii-11-1-1112-2−ii-1-111−i−iii2-22i−2i0000000000000000-1-111−i−iii00000000
χ3622-22-2-2-2222i−2i22i−2i2i2i−2i−2i-22-2-2-2-1-1112-22i−2i22i−2i2i2i−2i−2i-22−2i2i−i−iii-11-1-1112-2−ii-1-111−i−iii-22−2i2i000000000000000011-1-1ii−i−i00000000
χ3722-22-2-2-2222i−2i22i−2i−2i−2i2i2i-22-2-2-222-2-2-222i−2i22i−2i−2i−2i2i2i00002i2i−2i−2i2-222-2-2-222i−2i-2-222−2i−2i2i2i000000000000000000000000000000000000
χ3822-22-2-2-2222i−2i22i−2i−2i−2i2i2i-22-2-2-2-1-111-222i−2i22i−2i−2i−2i2i2i0000−i−iii-11-1-111-22−ii11-1-1ii−i−i00000000000000000000−i3i3i3−i33−3−3300000000
χ3922-22-2-2-2222i−2i22i−2i−2i−2i2i2i-22-2-2-2-1-111-222i−2i22i−2i−2i−2i2i2i0000−i−iii-11-1-111-22−ii11-1-1ii−i−i00000000000000000000i3−i3−i3i3−333−300000000
χ4022-22-2-2-222−2i2i2−2i2i2i2i−2i−2i-22-2-2-222-2-2-22−2i2i2−2i2i2i2i−2i−2i0000−2i−2i2i2i2-222-2-2-22−2i2i-2-2222i2i−2i−2i000000000000000000000000000000000000
χ4122-22-2-2-222−2i2i2−2i2i2i2i−2i−2i-22-2-2-2-1-111-22−2i2i2−2i2i2i2i−2i−2i0000ii−i−i-11-1-111-22i−i11-1-1−i−iii00000000000000000000−i3i3i3−i3−333−300000000
χ4222-22-2-2-222−2i2i2−2i2i2i2i−2i−2i-22-2-2-2-1-111-22−2i2i2−2i2i2i2i−2i−2i0000ii−i−i-11-1-111-22i−i11-1-1−i−iii00000000000000000000i3−i3−i3i33−3−3300000000
χ4322-22-2-2-222−2i2i2−2i2i−2i−2i2i2i-22-2-2-2-1-1112-2−2i2i2−2i2i−2i−2i2i2i2-2−2i2iii−i−i-11-1-1112-2i−i-1-111ii−i−i2-2−2i2i0000000000000000-1-111ii−i−i00000000
χ4422-22-2-2-222−2i2i2−2i2i−2i−2i2i2i-22-2-2-2-1-1112-2−2i2i2−2i2i−2i−2i2i2i-222i−2iii−i−i-11-1-1112-2i−i-1-111ii−i−i-222i−2i000000000000000011-1-1−i−iii00000000
χ453333333-1-1333333333-1-1-1-1-1000033-1-1-1-1-1-1-1-1-133330000000000-1-10000000000-1-1-1-111111111-1-1-1-1-1-1-1-1000000001111-1-1-1-1
χ463333333-1-1333333333-1-1-1-1-1000033-1-1-1-1-1-1-1-1-133330000000000-1-10000000000-1-1-1-1-1-1-1-1-1-1-1-11111111100000000-1-1-1-11111
χ473333333-1-1333333333-1-1-1-1-1000033-1-1-1-1-1-1-1-1-1-3-3-3-30000000000-1-10000000000111111111111-1-1-1-1-1-1-1-100000000-1-1-1-11111
χ483333333-1-1333333333-1-1-1-1-1000033-1-1-1-1-1-1-1-1-1-3-3-3-30000000000-1-100000000001111-1-1-1-1-1-1-1-111111111000000001111-1-1-1-1
χ493333333-1-1-3-33-3-3-3-3-3-3-1-1-1-1-100003311-111111133-3-30000000000-1-10000000000-1-111iiii−i−i−i−i−i−i−i−iiiii00000000ii−i−i−i−iii
χ503333333-1-1-3-33-3-3-3-3-3-3-1-1-1-1-100003311-111111133-3-30000000000-1-10000000000-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000−i−iiiii−i−i
χ513333333-1-1-3-33-3-3-3-3-3-3-1-1-1-1-100003311-1111111-3-3330000000000-1-1000000000011-1-1iiii−i−i−i−i−i−i−i−iiiii00000000−i−iiiii−i−i
χ523333333-1-1-3-33-3-3-3-3-3-3-1-1-1-1-100003311-1111111-3-3330000000000-1-1000000000011-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000ii−i−i−i−iii
χ5333-33-3-3-3-1-13i−3i33i−3i3i3i−3i−3i1-111100003-3−ii-1−ii−i−iii3-33i−3i0000000000-110000000000-11−iiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ5433-33-3-3-3-1-13i−3i33i−3i3i3i−3i−3i1-111100003-3−ii-1−ii−i−iii3-33i−3i0000000000-110000000000-11−ii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ5533-33-3-3-3-1-13i−3i33i−3i3i3i−3i−3i1-111100003-3−ii-1−ii−i−iii-33−3i3i0000000000-1100000000001-1i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ5633-33-3-3-3-1-13i−3i33i−3i3i3i−3i−3i1-111100003-3−ii-1−ii−i−iii-33−3i3i0000000000-1100000000001-1i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ5733-33-3-3-3-1-1−3i3i3−3i3i−3i−3i3i3i1-111100003-3i−i-1i−iii−i−i3-3−3i3i0000000000-110000000000-11i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ5833-33-3-3-3-1-1−3i3i3−3i3i−3i−3i3i3i1-111100003-3i−i-1i−iii−i−i3-3−3i3i0000000000-110000000000-11i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ5933-33-3-3-3-1-1−3i3i3−3i3i−3i−3i3i3i1-111100003-3i−i-1i−iii−i−i-333i−3i0000000000-1100000000001-1−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ6033-33-3-3-3-1-1−3i3i3−3i3i−3i−3i3i3i1-111100003-3i−i-1i−iii−i−i-333i−3i0000000000-1100000000001-1−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.