Finite Group Databasebeta

← Group #72252868

Character table — Group #72252868

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1122222222222222222888888888888888888888888888888888888999999181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818162162162162162162162162
order12233336666666666663333333336666666666666666666666666664488884881212121212121212121212121212121224242424242424242424242424242424242424242424242424242424242424241616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111111111111111111111111111111111111-1-1ii−i−i-1i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ61111111111111111111111111111111111111111111111111111111-1-1ii−i−i-1i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ71111111111111111111111111111111111111111111111111111111-1-1−i−iii-1−ii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ81111111111111111111111111111111111111111111111111111111-1-1−i−iii-1−ii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ911-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11-11-1
χ1011-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-11-11
χ1111-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111i−ii−i−ii−ii
χ1211-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−ii−iii−ii−i
χ1311-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1−ii11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13
χ1411-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i1−ii11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13
χ1511-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1i−i11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23
χ1611-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii1i−i11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−iζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23
χ172222-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122222222222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000000
χ182222-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-22-2-222-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111-2-2111111-2-211111100000000
χ192222-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-22i2i−2i−2i-22i−2i-2-2111111-2-21111112i2i−i−i−i−i−i−i2i2i−i−i−i−i−i−i−2i−2iiiiiii−2i−2iiiiiii00000000
χ202222-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2−2i−2i2i2i-2−2i2i-2-2111111-2-2111111−2i−2iiiiiii−2i−2iiiiiii2i2i−i−i−i−i−i−i2i2i−i−i−i−i−i−i00000000
χ21222-12-1-1-1-122-1-1-1-1-12-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222222222-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000
χ22222-12-1-1-1-122-1-1-1-1-12-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-2-2-2-22-2-2-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-2111111-2-2111111-2-2111100000000
χ23222-12-1-1-1-122-1-1-1-1-12-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-22i2i−2i−2i-22i−2i11-2-2111111-2-21111−i−i2i2i−i−i−i−i−i−i2i2i−i−i−i−iii−2i−2iiiiiii−2i−2iiiii00000000
χ24222-12-1-1-1-122-1-1-1-1-12-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2−2i−2i2i2i-2−2i2i11-2-2111111-2-21111ii−2i−2iiiiiii−2i−2iiiii−i−i2i2i−i−i−i−i−i−i2i2i−i−i−i−i00000000
χ25222-1-12-1-1-1-1-122-1-1-1-12-12-1-1-1-122-1-12-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1222222222-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-100000000
χ26222-1-12-1-1-1-1-122-1-1-1-12-12-1-1-1-122-1-12-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-122-2-2-2-22-2-2-1-1-1-122-1-1-1-1-1-122-1-11111-2-2111111-2-2111111-2-2111111-2-21100000000
χ27222-1-12-1-1-1-1-122-1-1-1-12-12-1-1-1-122-1-12-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-2-22i2i−2i−2i-22i−2i1111-2-2111111-2-211−i−i−i−i2i2i−i−i−i−i−i−i2i2i−i−iiiii−2i−2iiiiiii−2i−2iii00000000
χ28222-1-12-1-1-1-1-122-1-1-1-12-12-1-1-1-122-1-12-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-2-2−2i−2i2i2i-2−2i2i1111-2-2111111-2-211iiii−2i−2iiiiiii−2i−2iii−i−i−i−i2i2i−i−i−i−i−i−i2i2i−i−i00000000
χ29222-1-1-12-1-1-1-1-1-122-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222222222222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12200000000
χ30222-1-1-12-1-1-1-1-1-122-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-22-2-2-1-1-1-1-1-122-1-1-1-1-1-122111111-2-2111111-2-2111111-2-2111111-2-200000000
χ31222-1-1-12-1-1-1-1-1-122-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-2-22i2i−2i−2i-22i−2i111111-2-2111111-2-2−i−i−i−i−i−i2i2i−i−i−i−i−i−i2i2iiiiiii−2i−2iiiiiii−2i−2i00000000
χ32222-1-1-12-1-1-1-1-1-122-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2−2i−2i2i2i-2−2i2i111111-2-2111111-2-2iiiiii−2i−2iiiiiii−2i−2i−i−i−i−i−i−i2i2i−i−i−i−i−i−i2i2i00000000
χ3322-22-1-1-1-2-21111112-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-2111111111111222222-2-2-2-2-211111122-1-1-1-1-1-122-1-1-1-1-1-1-2-211111122-1-1-1-1-1-1-2-211111100000000
χ3422-22-1-1-1-2-21111112-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-211111111111122-2-2-2-2-222-2-211111122-1-1-1-1-1-1-2-211111122-1-1-1-1-1-1-2-211111122-1-1-1-1-1-100000000
χ3522-22-1-1-1-2-21111112-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-2111111111111-2-22i2i−2i−2i2−2i2i22-1-1-1-1-1-1-2-21111112i2i−i−i−i−i−i−i−2i−2iiiiiii−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000
χ3622-22-1-1-1-2-21111112-1-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-2111111111111-2-2−2i−2i2i2i22i−2i22-1-1-1-1-1-1-2-2111111−2i−2iiiiiii2i2i−i−i−i−i−i−i2i2i−i−i−i−i−i−i−2i−2iiiiiii00000000
χ3722-2-12-1-111-2-21111-12-1-12-1-122-1-1-1-12-1-122-1-1-1-1-2-21111-2-2-2-211111111222222-2-2-211-2-21111-1-122-1-1-1-1-1-122-1-1-1-111-2-21111-1-122-1-1-1-111-2-2111100000000
χ3822-2-12-1-111-2-21111-12-1-12-1-122-1-1-1-12-1-122-1-1-1-1-2-21111-2-2-2-21111111122-2-2-2-2-22211-2-21111-1-122-1-1-1-111-2-21111-1-122-1-1-1-111-2-21111-1-122-1-1-1-100000000
χ3922-2-12-1-111-2-21111-12-1-12-1-122-1-1-1-12-1-122-1-1-1-1-2-21111-2-2-2-211111111-2-22i2i−2i−2i2−2i2i-1-122-1-1-1-111-2-21111−i−i2i2i−i−i−i−iii−2i−2iiiiiii−2i−2iiiii−i−i2i2i−i−i−i−i00000000
χ4022-2-12-1-111-2-21111-12-1-12-1-122-1-1-1-12-1-122-1-1-1-1-2-21111-2-2-2-211111111-2-2−2i−2i2i2i22i−2i-1-122-1-1-1-111-2-21111ii−2i−2iiiii−i−i2i2i−i−i−i−i−i−i2i2i−i−i−i−iii−2i−2iiiii00000000
χ4122-2-1-12-11111-2-211-1-12-12-1-1-1-122-1-12-1-1-1-122-1-1-2-211111111-2-2-2-21111222222-2-2-21111-2-211-1-1-1-122-1-1-1-1-1-122-1-11111-2-211-1-1-1-122-1-11111-2-21100000000
χ4222-2-1-12-11111-2-211-1-12-12-1-1-1-122-1-12-1-1-1-122-1-1-2-211111111-2-2-2-2111122-2-2-2-2-2221111-2-211-1-1-1-122-1-11111-2-211-1-1-1-122-1-11111-2-211-1-1-1-122-1-100000000
χ4322-2-1-12-11111-2-211-1-12-12-1-1-1-122-1-12-1-1-1-122-1-1-2-211111111-2-2-2-21111-2-22i2i−2i−2i2−2i2i-1-1-1-122-1-11111-2-211−i−i−i−i2i2i−i−iiiii−2i−2iiiiiii−2i−2iii−i−i−i−i2i2i−i−i00000000
χ4422-2-1-12-11111-2-211-1-12-12-1-1-1-122-1-12-1-1-1-122-1-1-2-211111111-2-2-2-21111-2-2−2i−2i2i2i22i−2i-1-1-1-122-1-11111-2-211iiii−2i−2iii−i−i−i−i2i2i−i−i−i−i−i−i2i2i−i−iiiii−2i−2iii00000000
χ4522-2-1-1-12111111-2-2-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-122-2-2111111111111-2-2-2-2222222-2-2-2111111-2-2-1-1-1-1-1-122-1-1-1-1-1-122111111-2-2-1-1-1-1-1-122111111-2-200000000
χ4622-2-1-1-12111111-2-2-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-122-2-2111111111111-2-2-2-222-2-2-2-2-222111111-2-2-1-1-1-1-1-122111111-2-2-1-1-1-1-1-122111111-2-2-1-1-1-1-1-12200000000
χ4722-2-1-1-12111111-2-2-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-122-2-2111111111111-2-2-2-2-2-22i2i−2i−2i2−2i2i-1-1-1-1-1-122111111-2-2−i−i−i−i−i−i2i2iiiiiii−2i−2iiiiiii−2i−2i−i−i−i−i−i−i2i2i00000000
χ4822-2-1-1-12111111-2-2-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-122-2-2111111111111-2-2-2-2-2-2−2i−2i2i2i22i−2i-1-1-1-1-1-122111111-2-2iiiiii−2i−2i−i−i−i−i−i−i2i2i−i−i−i−i−i−i2i2iiiiiii−2i−2i00000000
χ492-20222200000000-2-2-2-2222222222-2-2-2-2-2-2-2-2-20000000000000000002i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000002i−2i2i−2i2i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ502-20222200000000-2-2-2-2222222222-2-2-2-2-2-2-2-2-20000000000000000002i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000002i−2i2i−2i2i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.