Finite Group Databasebeta

← Group #13147030

Character table — Group #13147030

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111111111111111111166666666666666666666121212121212121212121212181818181818181818181818181818181818181818181818242424242424242424242424242424242424242424242424363636363636363636363636
order123344668888121212122424242424242424234666881212121224242424242424246661212122424242424244444888812121212121212122424242424242424333666121212121212242424242424242424242424246688121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ411111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ51111-1-111ii−i−i-1-1-1-1iiii−i−i−i−i-1111-1-1i−i-1-111ii−i−iii−i−i-1-1-1111iii−i−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-111i−i-1-1ii−i−i
χ61111-1-111ii−i−i-1-1-1-1iiii−i−i−i−i-1111-1-1i−i-1-111ii−i−iii−i−i-1-1-1111iii−i−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-11111111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-11-1-1−ii11−i−iii
χ71111-1-111−i−iii-1-1-1-1−i−i−i−iiiii-1111-1-1−ii-1-111−i−iii−i−iii-1-1-1111−i−i−iiiiii−i−i-1-111iiii−i−i−i−i-1-1-1-11111111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-11-1-1i−i11ii−i−i
χ81111-1-111−i−iii-1-1-1-1−i−i−i−iiiii-1111-1-1−ii-1-111−i−iii−i−iii-1-1-1111−i−i−iiii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii1-111−ii-1-1−i−iii
χ922222222222222222222222222222222222222222222222222222222000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ102222222222222222222222222-12-12222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-1000000000000
χ112222222222222222222222222-12-12222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-12-1-12-1-1-122-1-1-1-122-1-1-1-122-1-1000000000000
χ122222222222222222222222222-12-12222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-122000000000000
χ1322222222-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000
χ1422222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-122-2-2-1-122-2-2-2-21111-1-1-1-1-1-11111110000000000000000000000002-1-12-1-122-1-1-1-1-2-21111-2-21111000000000000
χ1522222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-122-2-2-1-122-2-2-2-21111-1-1-1-1-1-1111111000000000000000000000000-12-1-12-1-1-122-1-111-2-21111-2-211000000000000
χ1622222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-122-2-2-1-122-2-2-2-21111-1-1-1-1-1-1111111000000000000000000000000-1-12-1-12-1-1-1-1221111-2-21111-2-2000000000000
χ172222-2-2222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i-2222-2-22i−2i-2-2222i2i−2i−2i2i2i−2i−2i-2-2-22222i2i2i−2i−2i−2i000000000000000000000000-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiii000000000000
χ182222-2-2222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-12-1-2-22i−2i11222i2i−2i−2i−i−iii111-1-1-1−i−i−iiii0000000000000000000000002-1-12-1-1-2-211112i2i−i−i−i−i−2i−2iiiii000000000000
χ192222-2-2222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-12-1-2-22i−2i11222i2i−2i−2i−i−iii111-1-1-1−i−i−iiii000000000000000000000000-12-1-12-111-2-211−i−i2i2i−i−iii−2i−2iii000000000000
χ202222-2-2222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-12-1-2-22i−2i11222i2i−2i−2i−i−iii111-1-1-1−i−i−iiii000000000000000000000000-1-12-1-121111-2-2−i−i−i−i2i2iiiii−2i−2i000000000000
χ212222-2-222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2222-2-2−2i2i-2-222−2i−2i2i2i−2i−2i2i2i-2-2-2222−2i−2i−2i2i2i2i000000000000000000000000-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i000000000000
χ222222-2-222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-12-1-2-2−2i2i1122−2i−2i2i2iii−i−i111-1-1-1iii−i−i−i0000000000000000000000002-1-12-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i000000000000
χ232222-2-222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-12-1-2-2−2i2i1122−2i−2i2i2iii−i−i111-1-1-1iii−i−i−i000000000000000000000000-12-1-12-111-2-211ii−2i−2iii−i−i2i2i−i−i000000000000
χ242222-2-222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-12-1-2-2−2i2i1122−2i−2i2i2iii−i−i111-1-1-1iii−i−i−i000000000000000000000000-1-12-1-121111-2-2iiii−2i−2i−i−i−i−i2i2i000000000000
χ252-2222i−2i-2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i2i−2i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13020-200002i−2i0000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000001−i−1+i1+i−1−i−i2i22−21−i1−i−1+i−1+i1+i1+i−1−i−1−i−i2−i2i2i222−2−2-1-1-1111i−ii−ii−iζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13000000000000
χ262-2222i−2i-2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i2i−2i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13020-200002i−2i0000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−1+i1−i−1−i1+ii2−i2−22−1+i−1+i1−i1−i−1−i−1−i1+i1+ii2i2−i2−i2−2−222-1-1-1111i−ii−ii−iζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13000000000000
χ272-2222i−2i-2-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i2i−2i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13020-200002i−2i000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000001−i−1+i1+i−1−ii2−i2−221−i1−i−1+i−1+i1+i1+i−1−i−1−ii2i2−i2−i2−2−222-1-1-1111i−ii−ii−i−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13000000000000
χ282-2222i−2i-2-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i2i−2i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13020-200002i−2i000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000−1+i1−i−1−i1+i−i2i22−2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−i2−i2i2i222−2−2-1-1-1111i−ii−ii−i−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13000000000000
χ292-222−2i2i-2-2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2i−2i2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23020-20000−2i2i000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000001+i−1−i1−i−1+ii2−i22−21+i1+i−1−i−1−i1−i1−i−1+i−1+ii2i2−i2−i222−2−2-1-1-1111−ii−ii−ii−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23000000000000
χ302-222−2i2i-2-2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2i−2i2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23020-20000−2i2i000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−1−i1+i−1+i1−i−i2i2−22−1−i−1−i1+i1+i−1+i−1+i1−i1−i−i2−i2i2i2−2−222-1-1-1111−ii−ii−ii−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23000000000000
χ312-222−2i2i-2-22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2i−2i2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23020-20000−2i2i0000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000001+i−1−i1−i−1+i−i2i2−221+i1+i−1−i−1−i1−i1−i−1+i−1+i−i2−i2i2i2−2−222-1-1-1111−ii−ii−iiζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23000000000000
χ322-222−2i2i-2-22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2i−2i2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23020-20000−2i2i0000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−1−i1+i−1+i1−ii2−i22−2−1−i−1−i1+i1+i−1+i−1+i1−i1−ii2i2−i2−i222−2−2-1-1-1111−ii−ii−iiζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23000000000000
χ33333333333333333333333333-13-13-1-1-1-133-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1
χ34333333333333333333333333-13-13-1-1-1-133-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000111111111111
χ3533333333-3-3-3-33333-3-3-3-3-3-3-3-3-13-13-1-11133-1-11111-3-3-3-3-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-10000000000000000000000001111-1-111-1-1-1-1
χ3633333333-3-3-3-33333-3-3-3-3-3-3-3-3-13-13-1-11133-1-11111-3-3-3-3-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111000000000000000000000000-1-1-1-111-1-11111
χ373333-3-3333i3i−3i−3i-3-3-3-33i3i3i3i−3i−3i−3i−3i13-1311−ii-3-3-1-1−i−iii3i3i−3i−3i111-1-1-1−i−i−iiiiii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1000000000000000000000000-11-1-1−ii11−i−iii
χ383333-3-3333i3i−3i−3i-3-3-3-33i3i3i3i−3i−3i−3i−3i13-1311−ii-3-3-1-1−i−iii3i3i−3i−3i111-1-1-1−i−i−iiii−i−iii-1-111−i−i−i−iiiii-1-1-1-111110000000000000000000000001-111i−i-1-1ii−i−i
χ393333-3-333−3i−3i3i3i-3-3-3-3−3i−3i−3i−3i3i3i3i3i13-1311i−i-3-3-1-1ii−i−i−3i−3i3i3i111-1-1-1iii−i−i−iii−i−i-1-111iiii−i−i−i−i-1-1-1-111110000000000000000000000001-111−ii-1-1−i−iii
χ403333-3-333−3i−3i3i3i-3-3-3-3−3i−3i−3i−3i3i3i3i3i13-1311i−i-3-3-1-1ii−i−i−3i−3i3i3i111-1-1-1iii−i−i−i−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1000000000000000000000000-11-1-1i−i11ii−i−i
χ4133−3−3i32−3+3i3233−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323030−3−3i32−3+3i323300−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000011111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000000000000000000011−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ4233−3−3i32−3+3i3233−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323030−3−3i32−3+3i323300−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32000000000000000000000000-1-11+i321−i32-1-11+i321−i321+i321−i321+i321−i32
χ4333−3−3i32−3+3i3233−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-10-101+i321−i32-1-1001+i321−i321+i321−i321+i321−i3200002−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i311111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32000000000000000000000000-1-11+i321−i32-1-11+i321−i321+i321−i321+i321−i32
χ4433−3−3i32−3+3i3233−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-10-101+i321−i32-1-1001+i321−i321+i321−i321+i321−i3200002−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i3200000000000000000000000011−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ4533−3−3i32−3+3i3233−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i323030−3−3i32−3+3i32-3-300−3−3i32−3+3i323+3i323−3i323+3i323−3i3200000000000000001111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32000000000000000000000000-1-11+i321−i32111+i321−i32−1−i32−1+i32−1−i32−1+i32
χ4633−3−3i32−3+3i3233−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i323030−3−3i32−3+3i32-3-300−3−3i32−3+3i323+3i323−3i323+3i323−3i320000000000000000-1-1-1-111111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000000000000000000011−1−i32−1+i32-1-1−1−i32−1+i321+i321−i321+i321−i32
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.