Finite Group Databasebeta

← Group #13147021

Character table — Group #13147021

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111111122222233333333333366666666666666666666666666666666666666242424242424242424242424242424242424242424242424363636363636363636363636363636363636363636363636
order12334466121212128824242424224466661212121236666666881212121212121212242424242424242424242424242424242424242433366612121212121224242424242424242424242424446688881212121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111-1-1-1-1-1-111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ51111-1-111-1-1-1-1i−iii−i−i11-1-11111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iiiiiiiii−i−i−i−i−i−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-11-111i−ii−i-1-111-1-1ii−i−iii−i−i
χ61111-1-111-1-1-1-1i−iii−i−i11-1-11111-1-1-1-111111111i−i-1-1-1-1-1-1-1-1ii−i−iiiiiiiii−i−i−i−i−i−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-11-11-1-1−ii−ii11-1-111−i−iii−i−iii
χ71111-1-111-1-1-1-1−ii−i−iii11-1-11111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−i−i−i−i−i−i−iiiiiiiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii1-11-111−ii−ii-1-111-1-1−i−iii−i−iii
χ81111-1-111-1-1-1-1−ii−i−iii11-1-11111-1-1-1-111111111−ii-1-1-1-1-1-1-1-1−i−iii−i−i−i−i−i−i−i−iiiiiiiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-11-11-1-1i−ii−i11-1-111ii−i−iii−i−i
χ922222222222222222222222222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ10222222222222222222222222222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-1000000000000000000000000
χ11222222222222222222222222222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-1-122-1-1-1-122-1-1-1-122-1-1000000000000000000000000
χ12222222222222222222222222222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-122000000000000000000000000
χ13222222222222-2-2-2-2-2-222222222222222222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000
χ14222222222222-2-2-2-2-2-2222222222222-1-1-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-1-2-2-2-211111111111111112-1-12-1-122-1-1-1-1-2-21111-2-21111000000000000000000000000
χ15222222222222-2-2-2-2-2-2222222222222-1-1-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-12-1-12-1-1-122-1-111-2-21111-2-211000000000000000000000000
χ16222222222222-2-2-2-2-2-2222222222222-1-1-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-1-12-1-12-1-1-1-1221111-2-21111-2-2000000000000000000000000
χ172222-2-222-2-2-2-22i−2i2i2i−2i−2i22-2-22222-2-2-2-2222222222i−2i-2-2-2-2-2-2-2-22i2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiii000000000000000000000000
χ182222-2-222-2-2-2-22i−2i2i2i−2i−2i22-2-22222-2-2-2-2-1-1-1-1-1-1-1-12i−2i111111112i2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii2-1-12-1-1-2-211112i2i−i−i−i−i−2i−2iiiii000000000000000000000000
χ192222-2-222-2-2-2-22i−2i2i2i−2i−2i22-2-22222-2-2-2-2-1-1-1-1-1-1-1-12i−2i111111112i2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii-12-1-12-111-2-211−i−i2i2i−i−iii−2i−2iii000000000000000000000000
χ202222-2-222-2-2-2-22i−2i2i2i−2i−2i22-2-22222-2-2-2-2-1-1-1-1-1-1-1-12i−2i111111112i2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii-1-12-1-121111-2-2−i−i−i−i2i2iiiii−2i−2i000000000000000000000000
χ212222-2-222-2-2-2-2−2i2i−2i−2i2i2i22-2-22222-2-2-2-222222222−2i2i-2-2-2-2-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i000000000000000000000000
χ222222-2-222-2-2-2-2−2i2i−2i−2i2i2i22-2-22222-2-2-2-2-1-1-1-1-1-1-1-1−2i2i11111111−2i−2i2i2iiiiiiiii−i−i−i−i−i−i−i−i2-1-12-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i000000000000000000000000
χ232222-2-222-2-2-2-2−2i2i−2i−2i2i2i22-2-22222-2-2-2-2-1-1-1-1-1-1-1-1−2i2i11111111−2i−2i2i2iiiiiiiii−i−i−i−i−i−i−i−i-12-1-12-111-2-211ii−2i−2iii−i−i2i2i−i−i000000000000000000000000
χ242222-2-222-2-2-2-2−2i2i−2i−2i2i2i22-2-22222-2-2-2-2-1-1-1-1-1-1-1-1−2i2i11111111−2i−2i2i2iiiiiiiii−i−i−i−i−i−i−i−i-1-12-1-121111-2-2iiii−2i−2i−i−i−i−i2i2i000000000000000000000000
χ252-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i2222-2-2-2-2002i2i2i−2i−2i−2i2i−2i00000000000000000000222-2-2-22i−2i2i−2i2i−2i000000000000000000000000000000000000
χ262-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i2222-2-2-2-2002i2i2i−2i−2i−2i2i−2i00000000000000000000-1-1-1111−ii−ii−ii−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ272-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i2222-2-2-2-2002i2i2i−2i−2i−2i2i−2i00000000000000000000-1-1-1111−ii−ii−iiζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ282-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i-1-1-1-1111100−i−i−iiii−ii0000−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ132-1-1-2112i−2i−ii−ii00−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ292-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i-1-1-1-1111100−i−i−iiii−ii0000−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13-12-11-21−ii2i−2i−iiζ7−ζ23−ζ7+ζ2300−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ302-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i-1-1-1-1111100−i−i−iiii−ii0000−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13-1-1211-2−ii−ii2i−2i−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000000000000000000000
χ312-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i-1-1-1-1111100−i−i−iiii−ii0000ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ132-1-1-2112i−2i−ii−ii00ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ322-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i-1-1-1-1111100−i−i−iiii−ii0000ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13-12-11-21−ii2i−2i−ii−ζ7+ζ23ζ7−ζ2300ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ332-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i-1-1-1-1111100−i−i−iiii−ii0000ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13-1-1211-2−ii−ii2i−2iζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000000000000000000000
χ342-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i2222-2-2-2-200−2i−2i−2i2i2i2i−2i2i00000000000000000000222-2-2-2−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ352-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i2222-2-2-2-200−2i−2i−2i2i2i2i−2i2i00000000000000000000-1-1-1111i−ii−ii−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ362-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i2222-2-2-2-200−2i−2i−2i2i2i2i−2i2i00000000000000000000-1-1-1111i−ii−ii−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ372-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i-1-1-1-1111100iii−i−i−ii−i0000ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ232-1-1-211−2i2ii−ii−i00ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ382-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i-1-1-1-1111100iii−i−i−ii−i0000ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23-12-11-21i−i−2i2ii−i−ζ5+ζ13ζ5−ζ1300ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ392-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i-1-1-1-1111100iii−i−i−ii−i0000ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23-1-1211-2i−ii−i−2i2iζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000000000000000000000
χ402-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i-1-1-1-1111100iii−i−i−ii−i0000−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ232-1-1-211−2i2ii−ii−i00−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ412-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i-1-1-1-1111100iii−i−i−ii−i0000−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23-12-11-21i−i−2i2ii−iζ5−ζ13−ζ5+ζ1300−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ2300ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ422-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i-1-1-1-1111100iii−i−i−ii−i0000−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23-1-1211-2i−ii−i−2i2i−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000000000000000000000
χ43333333333333333333-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-13-1-1-1-1-1-1-1-133-1-1-1-13-1-1-13-1-1-13-1-1-13-1-1-100000000000000000000000011-1-11111-1-111-1-1-1-11111-1-1-1-1
χ44333333333333333333-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-13-1-1-1-1-1-1-1-133-1-1-1-13-1-1-13-1-1-13-1-1-13-1-1-1000000000000000000000000-1-111-1-1-1-111-1-11111-1-1-1-11111
χ45333333333333-3-3-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-1311-1-1-1-1-1-1331111-3111-3111-3111-311100000000000000000000000011-1-111-1-11111-1-1-1-1-1-1-1-11111
χ46333333333333-3-3-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-1311-1-1-1-1-1-1331111-3111-3111-3111-3111000000000000000000000000-1-111-1-111-1-1-1-111111111-1-1-1-1
χ473333-3-333-3-3-3-33i−3i3i3i−3i−3i-1-111-1-1-1-111113-1-1-1-1-1-13−ii111111-3-3−i−iii3i−i−i−i3i−i−i−i−3iiii−3iiii0000000000000000000000001-1-1111i−i−ii-1-1-1-111ii−i−i−i−iii
χ483333-3-333-3-3-3-33i−3i3i3i−3i−3i-1-111-1-1-1-111113-1-1-1-1-1-13−ii111111-3-3−i−iii3i−i−i−i3i−i−i−i−3iiii−3iiii000000000000000000000000-111-1-1-1−iii−i1111-1-1−i−iiiii−i−i
χ493333-3-333-3-3-3-3−3i3i−3i−3i3i3i-1-111-1-1-1-111113-1-1-1-1-1-13i−i111111-3-3ii−i−i−3iiii−3iiii3i−i−i−i3i−i−i−i0000000000000000000000001-1-1111−iii−i-1-1-1-111−i−iiiii−i−i
χ503333-3-333-3-3-3-3−3i3i−3i−3i3i3i-1-111-1-1-1-111113-1-1-1-1-1-13i−i111111-3-3ii−i−i−3iiii−3iiii3i−i−i−i3i−i−i−i000000000000000000000000-111-1-1-1i−i−ii1111-1-1ii−i−i−i−iii
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.