Finite Group Databasebeta

← Group #11785565

Character table — Group #11785565

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222244444444444444444444888888121212121212121212121212121212121212121212121212181818182424242436364848484872727272
order12442488883366661212121212122424242424242424612242424242244666688881212121224242424242424242244888888242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ5111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ6111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ7111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-111-1-1-1-111
χ8111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1
χ911-1-1-1111-1-111-1-111-1-111-1-11111-1-1-1-1-1111-1-11-11-111-1-111-1-111-1-11111-1-1-1-11-11-1i−ii−i1-1i−ii−ii−ii−i
χ1011-1-1-1111-1-111-1-111-1-111-1-11111-1-1-1-1-1111-1-11-11-111-1-111-1-111-1-11111-1-1-1-11-11-1−ii−ii1-1−ii−ii−ii−ii
χ1111-1-1-1111-1-111-1-111-1-111-1-11111-1-1-1-1-1111-1-1-11-11-1-111-1-111-1-111-1-1-1-111111-11-1i−ii−i1-1i−ii−i−ii−ii
χ1211-1-1-1111-1-111-1-111-1-111-1-11111-1-1-1-1-1111-1-1-11-11-1-111-1-111-1-111-1-1-1-111111-11-1−ii−ii1-1−ii−iii−ii−i
χ1311-1-1-11-1-11111-1-111-1-111-1-1-1-1-1-11111-11-1-1111-11-111-1-1-1-11111-1-1-1-1-1-111111-11-1i−i−ii-11i−i−iii−i−ii
χ1411-1-1-11-1-11111-1-111-1-111-1-1-1-1-1-11111-11-1-1111-11-111-1-1-1-11111-1-1-1-1-1-111111-11-1−iii−i-11−iii−i−iii−i
χ1511-1-1-11-1-11111-1-111-1-111-1-1-1-1-1-11111-11-1-111-11-11-1-11111-1-1-1-1111111-1-1-1-11-11-1i−i−ii-11i−i−ii−iii−i
χ1611-1-1-11-1-11111-1-111-1-111-1-1-1-1-1-11111-11-1-111-11-11-1-11111-1-1-1-1111111-1-1-1-11-11-1−iii−i-11−iii−ii−i−ii
χ17222222222222222222222222222222222222000000000000000000000000-2-2-2-20000-2-200000000
χ18222222-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000-2-2-2-200002200000000
χ192222-2-2000022-2-22222-2-22200000000-2-20000000000002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i2-2-2200000000000000
χ202222-2-2000022-2-22222-2-22200000000-2-2000000000000−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i2-2-2200000000000000
χ212222-2-2000022-2-22222-2-22200000000-2-200002-2-2222-2-20000-2-22200000000-222-200000000000000
χ222222-2-2000022-2-22222-2-22200000000-2-20000-222-2-2-222000022-2-200000000-222-200000000000000
χ2322-2-22-20000222222-2-2-2-2-2-2000000002-20000000000002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i22-2-200000000000000
χ2422-2-22-20000222222-2-2-2-2-2-2000000002-2000000000000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i22-2-200000000000000
χ2522-2-22-20000222222-2-2-2-2-2-2000000002-2000022-2-222220000-2-2-2-200000000-2-22200000000000000
χ2622-2-22-20000222222-2-2-2-2-2-2000000002-20000-2-222-2-2-2-20000222200000000-2-22200000000000000
χ2722-2-2-2222-2-222-2-222-2-222-2-22222-2-2-2-2-2222-2-2000000000000000000000000-22-220000-2200000000
χ2822-2-2-22-2-22222-2-222-2-222-2-2-2-2-2-22222-22-2-222000000000000000000000000-22-2200002-200000000
χ2944444444441-2-2-21-2-2-2-2-211-2-2-2-2-2-2-2-21111110000000000000000000000000000222200-1-1-1-10000
χ3044444444441-2-2-21-2-2-2-2-211-2-2-2-2-2-2-2-21111110000000000000000000000000000-2-2-2-20011110000
χ314444444444-2111-211111-2-211111111-2-2-2-2-2-22222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ324444444444-2111-211111-2-211111111-2-2-2-2-2-2-2-2-2-21111-2-2-2-2111111111111000000000000000000
χ33444444-4-4-4-41-2-2-21-2-2-2-2-2112222222211-1-1-1-1000000000000000000000000000022-2-200-1-1110000
χ34444444-4-4-4-41-2-2-21-2-2-2-2-2112222222211-1-1-1-10000000000000000000000000000-2-2220011-1-10000
χ35444444-4-4-4-4-2111-211111-2-2-1-1-1-1-1-1-1-1-2-222222222-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000000000
χ36444444-4-4-4-4-2111-211111-2-2-1-1-1-1-1-1-1-1-2-22222-2-2-2-2111122221111-1-1-1-1-1-1-1-1000000000000000000
χ374444-4-40000-21-1-1-2111-1-1-2-23i3i−3i−3i3i3i−3i−3i2200002-2-22-1-1112i−2i2i−2i11-1-1−i−iii−i−iii000000000000000000
χ384444-4-40000-21-1-1-2111-1-1-2-23i3i−3i−3i3i3i−3i−3i220000-222-211-1-1−2i2i−2i2i-1-111ii−i−iii−i−i000000000000000000
χ394444-4-40000-21-1-1-2111-1-1-2-2−3i−3i3i3i−3i−3i3i3i2200002-2-22-1-111−2i2i−2i2i11-1-1ii−i−iii−i−i000000000000000000
χ404444-4-40000-21-1-1-2111-1-1-2-2−3i−3i3i3i−3i−3i3i3i220000-222-211-1-12i−2i2i−2i-1-111−i−iii−i−iii000000000000000000
χ4144-4-44-40000-2111-21-1-1-1-1223i3i−3i−3i−3i−3i3i3i-22000022-2-2-1-1-1-12i−2i−2i2i1111−i−iiiii−i−i000000000000000000
χ4244-4-44-40000-2111-21-1-1-1-1223i3i−3i−3i−3i−3i3i3i-220000-2-2221111−2i2i2i−2i-1-1-1-1ii−i−i−i−iii000000000000000000
χ4344-4-44-40000-2111-21-1-1-1-122−3i−3i3i3i3i3i−3i−3i-22000022-2-2-1-1-1-1−2i2i2i−2i1111ii−i−i−i−iii000000000000000000
χ4444-4-44-40000-2111-21-1-1-1-122−3i−3i3i3i3i3i−3i−3i-220000-2-22211112i−2i−2i2i-1-1-1-1−i−iiiii−i−i000000000000000000
χ4544-4-4-4444-4-41-2221-222-2-2-1-1-2-2-2-22222-1111-1-100000000000000000000000000002i−2i2i−2i00−ii−ii0000
χ4644-4-4-4444-4-41-2221-222-2-2-1-1-2-2-2-22222-1111-1-10000000000000000000000000000−2i2i−2i2i00i−ii−i0000
χ4744-4-4-4444-4-4-21-1-1-21-1-111221111-1-1-1-12-2-2-2222-22-2-1-11122-2-2-1-111-1-1-1-11111000000000000000000
χ4844-4-4-4444-4-4-21-1-1-21-1-111221111-1-1-1-12-2-2-222-22-2211-1-1-2-22211-1-11111-1-1-1-1000000000000000000
χ4944-4-4-44-4-4441-2221-222-2-2-1-12222-2-2-2-2-11-1-11100000000000000000000000000002i−2i−2i2i00−iii−i0000
χ5044-4-4-44-4-4441-2221-222-2-2-1-12222-2-2-2-2-11-1-1110000000000000000000000000000−2i2i2i−2i00i−i−ii0000
χ5144-4-4-44-4-444-21-1-1-21-1-11122-1-1-1-111112-222-2-22-22-2-1-111-2-222-1-1111111-1-1-1-1000000000000000000
χ5244-4-4-44-4-444-21-1-1-21-1-11122-1-1-1-111112-222-2-2-22-2211-1-122-2-211-1-1-1-1-1-11111000000000000000000
χ534-44i−4i0022−22−2i22i24400-4-44i−4i004i−4i22−2222−22−2i22i2−2i22i20022−22−2i22i2000000000000000000000000000000000000000000
χ544-44i−4i0022−22−2i22i2-213-32-1i−i3i−3i−2i2i−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ2300−22i2−i20000−i3i3−i3i300003−33−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ554-44i−4i0022−22−2i22i2-213-32-1i−i3i−3i−2i2i−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ2300−22i2−i20000i3−i3i3−i30000−33−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ564-44i−4i0022−22−2i22i2-21-332-1i−i−3i3i−2i2iζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ2300−22i2−i20000−i3i3i3−i30000−333−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ574-44i−4i0022−22−2i22i2-21-332-1i−i−3i3i−2i2iζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ2300−22i2−i20000i3−i3−i3i300003−3−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ584-44i−4i00−22222i2−2i24400-4-44i−4i004i−4i−2222−22222i2−2i22i2−2i200−22222i2−2i2000000000000000000000000000000000000000000
χ594-44i−4i00−22222i2−2i2-213-32-1i−i3i−3i−2i2i2ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23002−2−i2i20000−i3i3−i3i300003−33−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ604-44i−4i00−22222i2−2i2-213-32-1i−i3i−3i−2i2i2ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23002−2−i2i20000i3−i3i3−i30000−33−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ614-44i−4i00−22222i2−2i2-21-332-1i−i−3i3i−2i2i−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23002−2−i2i20000−i3i3i3−i30000−333−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ624-44i−4i00−22222i2−2i2-21-332-1i−i−3i3i−2i2i−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23002−2−i2i20000i3−i3−i3i300003−3−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ634-4−4i4i0022−222i2−2i24400-4-4−4i4i00−4i4i22−2222−222i2−2i22i2−2i20022−222i2−2i2000000000000000000000000000000000000000000
χ644-4−4i4i0022−222i2−2i2-213-32-1−ii−3i3i2i−2iζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ2300−22−i2i20000−i3i3−i3i30000−33−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ654-4−4i4i0022−222i2−2i2-213-32-1−ii−3i3i2i−2iζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ2300−22−i2i20000i3−i3i3−i300003−33−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ664-4−4i4i0022−222i2−2i2-21-332-1−ii3i−3i2i−2i−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ2300−22−i2i20000−i3i3i3−i300003−3−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ674-4−4i4i0022−222i2−2i2-21-332-1−ii3i−3i2i−2i−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ2300−22−i2i20000i3−i3−i3i30000−333−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ684-4−4i4i00−2222−2i22i24400-4-4−4i4i00−4i4i−2222−2222−2i22i2−2i22i200−2222−2i22i2000000000000000000000000000000000000000000
χ694-4−4i4i00−2222−2i22i2-213-32-1−ii−3i3i2i−2i−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23002−2i2−i20000−i3i3−i3i30000−33−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ704-4−4i4i00−2222−2i22i2-213-32-1−ii−3i3i2i−2i−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23002−2i2−i20000i3−i3i3−i300003−33−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ714-4−4i4i00−2222−2i22i2-21-332-1−ii3i−3i2i−2i2ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23002−2i2−i20000−i3i3i3−i300003−3−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ724-4−4i4i00−2222−2i22i2-21-332-1−ii3i−3i2i−2i2ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23002−2i2−i20000i3−i3−i3i30000−333−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ738888-8-800002-4442-4-4-4442200000000-2-20000000000000000000000000000000000000000000000
χ7488-8-88-800002-4-4-42-44444-2-2000000002-20000000000000000000000000000000000000000000000
χ758-88i−8i0042−42−4i24i22-400-24−4i4i002i−2i−2222−22222i2−2i22i2−2i2002−2−i2i2000000000000000000000000000000000000000000
χ768-88i−8i00−42424i2−4i22-400-24−4i4i002i−2i22−2222−22−2i22i2−2i22i200−22i2−i2000000000000000000000000000000000000000000
χ778-8−8i8i0042−424i2−4i22-400-244i−4i00−2i2i−2222−2222−2i22i2−2i22i2002−2i2−i2000000000000000000000000000000000000000000
χ788-8−8i8i00−4242−4i24i22-400-244i−4i00−2i2i22−2222−222i2−2i22i2−2i200−22−i2i2000000000000000000000000000000000000000000

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