Finite Group Databasebeta

← Group #10690507

Character table — Group #10690507

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order12224444344444444666121212121212121212121212246688888888888812121212121224242424242424242424242424242424888888242424242424242424242424242424248888224488888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ6111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ91111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11-1-1ii−i−i1111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-1i−iii−i−i1-1
χ101111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11-1-1ii−i−i1111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-111−ii−i−iii-11
χ111111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11-1-1ii−i−i-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1i−i−i−iii-11
χ121111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11-1-1ii−i−i-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111−iiii−i−i1-1
χ131111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11-1-1−i−iii1111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1−ii−i−iii−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-111i−iii−i−i-11
χ141111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11-1-1−i−iii1111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1−ii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-1−ii−i−iii1-1
χ151111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11-1-1−i−iii-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111−iiii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111i−i−i−iii1-1
χ161111-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11-1-1−i−iii-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111111111−iiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1−iiii−i−i-11
χ1722222222222-2-222-2-2222222222222222-2-2-2-2000000000000-2-2-2-2-2-20000000000000000000000000000000000000022220000-2-2000000
χ1822222222222-2-222-2-2222222222222222-2-2-2-2000000000000-2-2-2-2-2-200000000000000000000000000000000000000-2-2-2-2000022000000
χ19222222222-2-222-2-222222-2-2-2-22222-2-2-2-2-2-2-2-22222000000002222-2-20000000000000000-2-2000022-2-222-2-2000000000000000000000000
χ20222222222-2-222-2-222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-20000000000000000220000-2-222-2-222000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2-2-22222000000000000-2-2-2-2220000000000000000000000000000000000000000002-22-200000000
χ22222222222-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2-2-22222000000000000-2-2-2-222000000000000000000000000000000000000000000-22-2200000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2722222222-1-2-222-2-222-1-1-11111-1-1-1-11111-2-211222200000000-1-1-1-1113333−3−3−3−33333−3−3−3−3-2-20000-1-111-1-11133−3−333−3−30000000000000000
χ2822222222-1-2-222-2-222-1-1-11111-1-1-1-11111-2-211222200000000-1-1-1-111−3−3−3−33333−3−3−3−33333-2-20000-1-111-1-111−3−333−3−3330000000000000000
χ2922222222-1-2-222-2-222-1-1-11111-1-1-1-11111-2-211-2-2-2-200000000-1-1-1-1113333−3−3−3−33333−3−3−3−322000011-1-111-1-1−3−333−3−3330000000000000000
χ3022222222-1-2-222-2-222-1-1-11111-1-1-1-11111-2-211-2-2-2-200000000-1-1-1-111−3−3−3−33333−3−3−3−3333322000011-1-111-1-133−3−333−3−30000000000000000
χ312222-2-2-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-22-222000000000000-2-222-2-2000000000000000000000000000000000000002i2i−2i−2i0000−2i2i000000
χ322222-2-2-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-22-222000000000000-2-222-2-200000000000000000000000000000000000000−2i−2i2i2i00002i−2i000000
χ332222-2-2-2-22-2-22222-2-2222-2-2-2-2-2-2-2-222222-2222i2i−2i−2i0000000022-2-2-2-20000000000000000−2i2i00002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ342222-2-2-2-22-2-22222-2-2222-2-2-2-2-2-2-2-222222-222−2i−2i2i2i0000000022-2-2-2-200000000000000002i−2i0000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ352222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22222-22-2-2000000000000-2-222220000000000000000000000000000000000000000002-2-2200000000
χ362222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22222-22-2-2000000000000-2-22222000000000000000000000000000000000000000000-222-200000000
χ372222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-22112i2i−2i−2i2222-2-2-2-2-1-111-1-1-1-1-1-1-1-1-1-1111111112i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ382222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-22112i2i−2i−2i-2-2-2-22222-1-111-1-111111111-1-1-1-1-1-1-1-12i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ392222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-2211−2i−2i2i2i2222-2-2-2-2-1-111-1-1-1-1-1-1-1-1-1-111111111−2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ402222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-2211−2i−2i2i2i-2-2-2-22222-1-111-1-111111111-1-1-1-1-1-1-1-1−2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ412222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-12-2-1-12i2i−2i−2i00000000-1-111113333−3−3−3−3−3−3−3−33333−2i2i0000−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i30000000000000000
χ422222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-12-2-1-12i2i−2i−2i00000000-1-11111−3−3−3−333333333−3−3−3−3−2i2i0000−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i30000000000000000
χ432222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-12-2-1-1−2i−2i2i2i00000000-1-111113333−3−3−3−3−3−3−3−333332i−2i0000ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i30000000000000000
χ442222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-12-2-1-1−2i−2i2i2i00000000-1-11111−3−3−3−333333333−3−3−3−32i−2i0000ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i30000000000000000
χ4522-2-22i2i−2i−2i2002-2002i−2i2-2-200002i2i−2i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1322−2−2−i2−i2i2i22-22i−2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i2001+i−1−i1−i−1+i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ4622-2-22i2i−2i−2i2002-2002i−2i2-2-200002i2i−2i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2−222i2i2−i2−i22-22i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i200−1−i1+i−1+i1−i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ4722-2-22i2i−2i−2i2002-2002i−2i2-2-200002i2i−2i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1322−2−2−i2−i2i2i22-22i−2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i200−1−i1+i−1+i1−i−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ4822-2-22i2i−2i−2i2002-2002i−2i2-2-200002i2i−2i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2−222i2i2−i2−i22-22i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i2001+i−1−i1−i−1+i−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ4922-2-22i2i−2i−2i-1002-2002i−2i-11133−3−3−i−iii−i3−i3i3i300−i3i32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1322−2−2−i2−i2i2i2-11−ii3−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7001+i−1−i1−i−1+i−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ220000000000000000
χ5022-2-22i2i−2i−2i-1002-2002i−2i-11133−3−3−i−iii−i3−i3i3i300−i3i32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2−222i2i2−i2−i2-11−ii3−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700−1−i1+i−1+i1−i−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ220000000000000000
χ5122-2-22i2i−2i−2i-1002-2002i−2i-11133−3−3−i−iii−i3−i3i3i300−i3i3−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1322−2−2−i2−i2i2i2-11−ii3−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700−1−i1+i−1+i1−iζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ220000000000000000
χ5222-2-22i2i−2i−2i-1002-2002i−2i-11133−3−3−i−iii−i3−i3i3i300−i3i3−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2−222i2i2−i2−i2-11−ii3−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7001+i−1−i1−i−1+iζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ220000000000000000
χ5322-2-22i2i−2i−2i-1002-2002i−2i-111−3−333−i−iiii3i3−i3−i300i3−i32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1322−2−2−i2−i2i2i2-11−ii−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23001+i−1−i1−i−1+i−ζ7−ζ23ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ140000000000000000
χ5422-2-22i2i−2i−2i-1002-2002i−2i-111−3−333−i−iiii3i3−i3−i300i3−i32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2−222i2i2−i2−i2-11−ii−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300−1−i1+i−1+i1−i−ζ7−ζ23ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ140000000000000000
χ5522-2-22i2i−2i−2i-1002-2002i−2i-111−3−333−i−iiii3i3−i3−i300i3−i3−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1322−2−2−i2−i2i2i2-11−ii−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300−1−i1+i−1+i1−iζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ140000000000000000
χ5622-2-22i2i−2i−2i-1002-2002i−2i-111−3−333−i−iiii3i3−i3−i300i3−i3−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2−222i2i2−i2−i2-11−ii−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23001+i−1−i1−i−1+iζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ140000000000000000
χ5722-2-2−2i−2i2i2i2002-200−2i2i2-2-20000−2i−2i2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2322−2−2i2i2−i2−i22-2−2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i2001−i−1+i1+i−1−i−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ5822-2-2−2i−2i2i2i2002-200−2i2i2-2-20000−2i−2i2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2−222−i2−i2i2i22-2−2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i200−1+i1−i−1−i1+i−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.