Finite Group Databasebeta

← Group #10694001

Character table — Group #10694001

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order122222224444444434444444466666661212121212121212888888881212121212121212242424242424242424242424242424244444888812121212121212122424242424242424444444448888888844448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ1722222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-222-2-20000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-222-2-2220000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ212222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ2322222222-2-2-2-2-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000000000000000000000000000000022-2-2-2-2220000000000000000
χ2422222222-2-2-2-2-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000000000000000000000000000-2-22222-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1111111112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1111111112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000000000000000
χ2922-2-2-2-2222222-2-2-2-2222-2-222-2-2-2-2-2-22222222-2-2-2-20000000022-2-2-2-2220000000000000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ3022-2-2-2-2222222-2-2-2-2222-2-222-2-2-2-2-2-22222222-2-2-2-20000000022-2-2-2-222000000000000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ3122-2-2-2-2222222-2-2-2-22-2-222-2-222-2-2-2-22222222-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-22222-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
χ3222-2-2-2-2222222-2-2-2-22-2-222-2-222-2-2-2-22222222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-22222-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000
χ3322-2-2-2-2222222-2-2-2-2-1-2-222-2-2221111-1-1-1-1-1-1-111112i2i−2i−2i2i2i−2i−2i11-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii00000000−i3−i3i3i3−i3−i3i3i333−3−333−3−3000000000000000000000000
χ3422-2-2-2-2222222-2-2-2-2-1-2-222-2-2221111-1-1-1-1-1-1-111112i2i−2i−2i2i2i−2i−2i11-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii00000000i3i3−i3−i3i3i3−i3−i3−3−333−3−333000000000000000000000000
χ3522-2-2-2-2222222-2-2-2-2-1-2-222-2-2221111-1-1-1-1-1-1-11111−2i−2i2i2i−2i−2i2i2i11-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i00000000−i3−i3i3i3−i3−i3i3i3−3−333−3−333000000000000000000000000
χ3622-2-2-2-2222222-2-2-2-2-1-2-222-2-2221111-1-1-1-1-1-1-11111−2i−2i2i2i−2i−2i2i2i11-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i00000000i3i3−i3−i3i3i3−i3−i333−3−333−3−3000000000000000000000000
χ3722-2-2-2-222-2-2-2-22222222-2-2-2-222-2-2-2-2222-2-2-2-222220000000022-2-222-2-200000000000000000000000000000000000000000000000022-2-2-2-22200000000
χ3822-2-2-2-222-2-2-2-22222222-2-2-2-222-2-2-2-2222-2-2-2-222220000000022-2-222-2-2000000000000000000000000000000000000000000000000-2-22222-2-200000000
χ3922-2-2-2-222-2-2-2-222222-2-22222-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-222-2-222-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ4022-2-2-2-222-2-2-2-222222-2-22222-2-2-2-2-2-2222-2-2-2-22222-2-22222-2-2-2-222-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ4122-2-2-2-222-2-2-2-22222-1-2-22222-2-21111-1-1-11111-1-1-1-122-2-2-2-22211-1-111-1-1-1-1-1-111111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000000000000000
χ4222-2-2-2-222-2-2-2-22222-1-2-22222-2-21111-1-1-11111-1-1-1-122-2-2-2-22211-1-111-1-1-1-1-1-111111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000000000000000
χ4322-2-2-2-222-2-2-2-22222-1-2-22222-2-21111-1-1-11111-1-1-1-1-2-22222-2-211-1-111-1-11111-1-1-1-1-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000000000000000
χ4422-2-2-2-222-2-2-2-22222-1-2-22222-2-21111-1-1-11111-1-1-1-1-2-22222-2-211-1-111-1-11111-1-1-1-1-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000000000000000
χ452-222-2-22-22i2i−2i−2i2i−2i2i−2i20000000022-2-2-22-22i2i−2i−2i2i−2i2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i000000000000000000000000002i−2i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ462-222-2-22-22i2i−2i−2i2i−2i2i−2i20000000022-2-2-22-22i2i−2i−2i2i−2i2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00000000000000000000000000−2i2i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ472-222-2-22-22i2i−2i−2i2i−2i2i−2i20000000022-2-2-22-22i2i−2i−2i2i−2i2i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i000000000000000000000000002i−2i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ482-222-2-22-22i2i−2i−2i2i−2i2i−2i20000000022-2-2-22-22i2i−2i−2i2i−2i2i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00000000000000000000000000−2i2i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ492-222-2-22-2−2i−2i2i2i−2i2i−2i2i20000000022-2-2-22-2−2i−2i2i2i−2i2i−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i000000000000000000000000002i−2i00-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ502-222-2-22-2−2i−2i2i2i−2i2i−2i2i20000000022-2-2-22-2−2i−2i2i2i−2i2i−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00000000000000000000000000−2i2i002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ512-222-2-22-2−2i−2i2i2i−2i2i−2i2i20000000022-2-2-22-2−2i−2i2i2i−2i2i−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i000000000000000000000000002i−2i00-221+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ522-222-2-22-2−2i−2i2i2i−2i2i−2i2i20000000022-2-2-22-2−2i−2i2i2i−2i2i−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00000000000000000000000000−2i2i002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ532-22-22-2-222i−2i2i−2i2i−2i−2i2i22-22-22i−2i2i−2i2-22-2-2-222i−2i2i−2i−2i2i2i−2i000000002-22-22i−2i2i−2i0000000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ542-22-22-2-222i−2i2i−2i2i−2i−2i2i22-22-22i−2i2i−2i2-22-2-2-222i−2i2i−2i−2i2i2i−2i000000002-22-22i−2i2i−2i000000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ552-22-22-2-222i−2i2i−2i2i−2i−2i2i2-22-22−2i2i−2i2i2-22-2-2-222i−2i2i−2i−2i2i2i−2i00000000-22-22−2i2i−2i2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ562-22-22-2-222i−2i2i−2i2i−2i−2i2i2-22-22−2i2i−2i2i2-22-2-2-222i−2i2i−2i−2i2i2i−2i00000000-22-22−2i2i−2i2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ572-22-22-2-222i−2i2i−2i2i−2i−2i2i-1-22-22−2i2i−2i2i-11-1111-1−ii−iii−i−ii000000001-11-1i−ii−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ133−33−3−i3i3−i3i3−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13000000000000000000000000
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χ1144-44-44-4-44−4i4i−4i4i−4i4i4i−4i-24-44-4−4i4i−4i4i-22-2222-22i−2i2i−2i−2i2i2i−2i00000000-22-222i−2i2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ1154-4-44-44-444i−4i4i−4i−4i4i4i−4i-2-444-4−4i4i4i−4i2-22-222-2−2i2i−2i2i−2i2i2i−2i000000002-2-22−2i2i2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ1164-4-44-44-44−4i4i−4i4i4i−4i−4i4i-2-444-44i−4i−4i4i2-22-222-22i−2i2i−2i2i−2i−2i2i000000002-2-222i−2i−2i2i0000000000000000000000000000000000000000000000000000000000000000
χ1174-4-4-4444-44i4i−4i−4i−4i4i−4i4i-20000000022-2-22-22−2i−2i2i2i2i−2i2i−2i2−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i00000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000000000000000000000000000000000000000
χ1184-4-4-4444-44i4i−4i−4i−4i4i−4i4i-20000000022-2-22-22−2i−2i2i2i2i−2i2i−2i−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000000000000000000000000000000000000000
χ1194-4-4-4444-4−4i−4i4i4i4i−4i4i−4i-20000000022-2-22-222i2i−2i−2i−2i2i−2i2i2+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000000000000000000000000000000000000000000000
χ1204-4-4-4444-4−4i−4i4i4i4i−4i4i−4i-20000000022-2-22-222i2i−2i−2i−2i2i−2i2i−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i000000001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000000000000000000000000000000000000000

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