Finite Group Databasebeta

← Group #10693756

Character table — Group #10693756

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order122222224444444434444444466666661212121212121212888888881212121212121212242424242424242424242424242424244444888812121212121212122424242424242424888888888888888844448888
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
χ911111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−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
χ1011111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−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
χ1111111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−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
χ1211111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−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
χ1311111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ1722222222222222222-2-2-2-2-2-2-2-22222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-2222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
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
χ232222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ242222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ252222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ262222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22-2-222-2-2222222222-2-2-2-2-2-2-2-22i2i−2i−2i−2i−2i2i2i-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22-2-222-2-2222222222-2-2-2-2-2-2-2-2−2i−2i2i2i2i2i−2i−2i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
χ2922222222-2-2-2-2-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii000000000000000000000000
χ3022222222-2-2-2-2-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i000000000000000000000000
χ3122222222-2-2-2-2-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-111111111−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i000000000000000000000000
χ3222222222-2-2-2-2-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-111111111−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000000000000000
χ3322222222-2-2-2-2-2-2-2-2-1-2-222-2-222-1-1-1-1-1-1-1111111112i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000−i3−i3i3i3i3i3−i3−i333−3−3−3−333000000000000000000000000
χ3422222222-2-2-2-2-2-2-2-2-1-2-222-2-222-1-1-1-1-1-1-1111111112i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−3000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-2-1-2-222-2-222-1-1-1-1-1-1-111111111−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−3000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-2-1-2-222-2-222-1-1-1-1-1-1-111111111−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000i3i3−i3−i3−i3−i3i3i333−3−3−3−333000000000000000000000000
χ372222-2-2-2-22222-2-2-2-2222-2-2-2-222-2-2222-2-22222-2-2-2-20000000022-2-222-2-200000000000000000000000000000000000000000000000022-2-222-2-200000000
χ382222-2-2-2-22222-2-2-2-2222-2-2-2-222-2-2222-2-22222-2-2-2-20000000022-2-222-2-2000000000000000000000000000000000000000000000000-2-222-2-22200000000
χ392222-2-2-2-22222-2-2-2-22-2-22222-2-2-2-2222-2-22222-2-2-2-200000000-2-222-2-222000000000000000000000000000000000000000022-2-222-2-20000000000000000
χ402222-2-2-2-22222-2-2-2-22-2-22222-2-2-2-2222-2-22222-2-2-2-200000000-2-222-2-2220000000000000000000000000000000000000000-2-222-2-2220000000000000000
χ412222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2222-2-2-2-2-2-222220000000022-2-2-2-2220000000000000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ422222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2222-2-2-2-2-2-222220000000022-2-2-2-222000000000000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ432222-2-2-2-2-2-2-2-222222-2-2-2-22222-2-2222-2-2-2-2-2-2222200000000-2-22222-2-2000000000000000000000000000000000000000022-2-2-2-2220000000000000000
χ442222-2-2-2-2-2-2-2-222222-2-2-2-22222-2-2222-2-2-2-2-2-2222200000000-2-22222-2-20000000000000000000000000000000000000000-2-22222-2-20000000000000000
χ4522-2-22-22-22i2i−2i−2i2i−2i2i−2i2000000002-22-2-22-22i2i−2i−2i2i−2i2i−2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000000000000000000000002−22−2−i2i2−i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ4622-2-22-22-22i2i−2i−2i2i−2i2i−2i2000000002-22-2-22-22i2i−2i−2i2i−2i2i−2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23000000000000000000000000−22−22i2−i2i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ4722-2-22-22-22i2i−2i−2i2i−2i2i−2i2000000002-22-2-22-22i2i−2i−2i2i−2i2i−2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ230000000000000000000000002−22−2−i2i2−i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ4822-2-22-22-22i2i−2i−2i2i−2i2i−2i2000000002-22-2-22-22i2i−2i−2i2i−2i2i−2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000000000000000000000−22−22i2−i2i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ4922-2-22-22-2−2i−2i2i2i−2i2i−2i2i2000000002-22-2-22-2−2i−2i2i2i−2i2i−2i2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ130000000000000000000000002−22−2i2−i2i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ5022-2-22-22-2−2i−2i2i2i−2i2i−2i2i2000000002-22-2-22-2−2i−2i2i2i−2i2i−2i2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13000000000000000000000000−22−22−i2i2−i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ5122-2-22-22-2−2i−2i2i2i−2i2i−2i2i2000000002-22-2-22-2−2i−2i2i2i−2i2i−2i2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000000000000000000000002−22−2i2−i2i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ5222-2-22-22-2−2i−2i2i2i−2i2i−2i2i2000000002-22-2-22-2−2i−2i2i2i−2i2i−2i2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13000000000000000000000000−22−22−i2i2−i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ5322-2-2-22-222i2i−2i−2i−2i2i−2i2i200000000-222-2-2-222i2i−2i−2i−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23000000000000000000000000000000002−2−22−i2i2i2−i21−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ5422-2-2-22-222i2i−2i−2i−2i2i−2i2i200000000-222-2-2-222i2i−2i−2i−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000000000000000000000000000−222−2i2−i2−i2i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ5522-2-2-22-222i2i−2i−2i−2i2i−2i2i200000000-222-2-2-222i2i−2i−2i−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000000000000000000000000000002−2−22−i2i2i2−i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ5622-2-2-22-222i2i−2i−2i−2i2i−2i2i200000000-222-2-2-222i2i−2i−2i−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300000000000000000000000000000000−222−2i2−i2−i2i21−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ5722-2-2-22-22−2i−2i2i2i2i−2i2i−2i200000000-222-2-2-22−2i−2i2i2i2i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13000000000000000000000000000000002−2−22i2−i2−i2i21+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
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χ1084-44-4-444-4−4i4i−4i4i4i−4i−4i4i-2-44−4i4i4-44i−4i-222-222-22i−2i2i−2i−2i2i2i−2i000000002-2-22−2i2i2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ1094-4-4444-4-44-4-4444-4-4400000000-4-4-4-44444-4-4444-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1104-4-4444-4-44-4-4444-4-4-2000000002222-2-2-2-222-2-2-22200000000000000000000000023−23−232323−23−2323000000000000000000000000000000000000000000000000
χ1114-4-4444-4-44-4-4444-4-4-2000000002222-2-2-2-222-2-2-222000000000000000000000000−232323−23−232323−23000000000000000000000000000000000000000000000000
χ1124-4-4444-4-4-444-4-4-444400000000-4-4-4-4444-444-4-4-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1134-4-4444-4-4-444-4-4-444-2000000002222-2-2-22-2-2222-2-2000000000000000000000000−2i32i32i3−2i32i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ1144-4-4444-4-4-444-4-4-444-2000000002222-2-2-22-2-2222-2-20000000000000000000000002i3−2i3−2i32i3−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ1154-4-44-4-4444-4-44-4-44440000000044-4-44-4-44-4-44-4-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1164-4-44-4-4444-4-44-4-444-200000000-2-222-222-222-222-2-2000000000000000023−23−232323−23−232300000000000000000000000000000000000000000000000000000000
χ1174-4-44-4-4444-4-44-4-444-200000000-2-222-222-222-222-2-20000000000000000−232323−23−232323−2300000000000000000000000000000000000000000000000000000000
χ1184-4-44-4-444-444-444-4-440000000044-4-44-4-4-444-444-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1194-4-44-4-444-444-444-4-4-200000000-2-222-2222-2-22-2-2220000000000000000−2i32i32i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ1204-4-44-4-444-444-444-4-4-200000000-2-222-2222-2-22-2-22200000000000000002i3−2i3−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000

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