Finite Group Databasebeta

← Group #10693718

Character table — Group #10693718

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order122244442234444446666666121212121212121244888888881212121212121212242424242424242424242424242424244444888812121212121212122424242424242424888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111-1-1111-1-1111-1-111-1-1-1-1111-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1i−ii−i11-1-11-1i−i
χ101111-1-1-1-1-1-111-1-1111-1-1111-1-111-1-1-1-1111-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1−ii−ii-1-111-11−ii
χ111111-1-1-1-1-1-111-1-1111-1-1111-1-111-1-1-1-1111-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-11111i−ii−i11-1-1-11−ii
χ121111-1-1-1-1-1-111-1-1111-1-1111-1-111-1-1-1-1111-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-11111−ii−ii-1-1111-1i−i
χ131111-1-1-1-1-1-111-1-1111-1-1111-1-111-1-1-1-1111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-111iiii−i−i−i−i-1-1-1-11111i−ii−i-1-1111-1−ii
χ141111-1-1-1-1-1-111-1-1111-1-1111-1-111-1-1-1-1111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-111iiii−i−i−i−i-1-1-1-11111−ii−ii11-1-1-11i−i
χ151111-1-1-1-1-1-111-1-1111-1-1111-1-111-1-1-1-1111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1i−ii−i-1-111-11i−i
χ161111-1-1-1-1-1-111-1-1111-1-1111-1-111-1-1-1-1111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−ii−ii11-1-11-1−ii
χ17222222222222-2-22-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-200000000
χ18222222222222-2-22-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-22200000000
χ192222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ202222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ212222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ2322222222-2-22-222-222-2-2222-2-2-2-22222-2-2-2-222-2-222-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ2422222222-2-22-222-222-2-2222-2-2-2-22222-2-2-2-2-2-222-2-22222-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ2522222222-2-22-2-2-2-2-2-2-2-2222-2-2-2-22222-2-22200000000-2-22222-2-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ2622222222-2-22-2-2-2-2-2-2-2-2222-2-2-2-22222-2-22200000000-2-22222-2-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ2722222222-2-2-1-222-22211-1-1-11111-1-1-1-111-2-222-2-222-2-2-1-11111-1-1-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−3000000000000
χ2822222222-2-2-1-222-22211-1-1-11111-1-1-1-111-2-222-2-222-2-2-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−333000000000000
χ2922222222-2-2-1-222-22211-1-1-11111-1-1-1-111-2-2-2-222-2-222-1-11111-1-11111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−333000000000000
χ3022222222-2-2-1-222-22211-1-1-11111-1-1-1-111-2-2-2-222-2-222-1-11111-1-11111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−3000000000000
χ312222-2-2-2-2222-222-2-2-22222222-2-2-2-2-2-2-2-22-200000000-2-222-2-222000000000000000000000000000000000000000000002i−2i−2i2i0000
χ322222-2-2-2-2222-222-2-2-22222222-2-2-2-2-2-2-2-22-200000000-2-222-2-22200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ332222-2-2-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-2-222i2i−2i−2i−2i−2i2i2i22-2-222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ342222-2-2-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-2-22−2i−2i2i2i2i2i−2i−2i22-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ352222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-111111111-222i2i−2i−2i−2i−2i2i2i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−3000000000000
χ362222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-111111111-222i2i−2i−2i−2i−2i2i2i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000i3i3−i3−i3−i3−i3i3i333−3−3−3−333000000000000
χ372222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-111111111-22−2i−2i2i2i2i2i−2i−2i-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii00000000−i3−i3i3i3i3i3−i3−i333−3−3−3−333000000000000
χ382222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-111111111-22−2i−2i2i2i2i2i−2i−2i-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii00000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−3000000000000
χ392222-2-2-2-2-2-222222-2-2-2-2222-2-222-2-2-2-222-2200000000-2-2-2-2222200000000000000000000000000000000000000002i−2i−2i2i00000000
χ402222-2-2-2-2-2-222222-2-2-2-2222-2-222-2-2-2-222-2200000000-2-2-2-222220000000000000000000000000000000000000000−2i2i2i−2i00000000
χ412222-2-2-2-2-2-2-12-2-222211-1-1-111-1-11111-1-12-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii2i2i−2i−2i22-2-2−i−i−i−iiiii-1-1-1-11111000000000000
χ422222-2-2-2-2-2-2-12-2-222211-1-1-111-1-11111-1-12-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−2i−2i2i2i-2-222iiii−i−i−i−i1111-1-1-1-1000000000000
χ432222-2-2-2-2-2-2-12-2-222211-1-1-111-1-11111-1-12-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i2i2i−2i−2i-2-222−i−i−i−iiiii1111-1-1-1-1000000000000
χ442222-2-2-2-2-2-2-12-2-222211-1-1-111-1-11111-1-12-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−2i−2i2i2i22-2-2iiii−i−i−i−i-1-1-1-11111000000000000
χ4522-2-22i−2i2i−2i00202i−2i02-2002-2-200002i2i−2i−2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232-200002i−2i0000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ231+i−1−i1−i−1+i−i2i22−21+i−1−i1+i−1−i1−i−1+i1−i−1+i−i2i2−i2i22−22−2000000000000
χ4622-2-22i−2i2i−2i00202i−2i02-2002-2-200002i2i−2i−2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232-200002i−2i0000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−1−i1+i−1+i1−ii2−i2−22−1−i1+i−1−i1+i−1+i1−i−1+i1−ii2−i2i2−i2−22−22000000000000
χ4722-2-22i−2i2i−2i00202i−2i02-2002-2-200002i2i−2i−2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232-200002i−2i00002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ231+i−1−i1−i−1+ii2−i2−221+i−1−i1+i−1−i1−i−1+i1−i−1+ii2−i2i2−i2−22−22000000000000
χ4822-2-22i−2i2i−2i00202i−2i02-2002-2-200002i2i−2i−2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232-200002i−2i00002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−1−i1+i−1+i1−i−i2i22−2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−i2i2−i2i22−22−2000000000000
χ4922-2-22i−2i2i−2i00-102i−2i02-2−i3i3-111−i3i33−3−i−iii3−30000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23-113−3−i3i3−ii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231+i−1−i1−i−1+i−i2i22−2−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ5022-2-22i−2i2i−2i00-102i−2i02-2−i3i3-111−i3i33−3−i−iii3−30000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23-113−3−i3i3−ii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−1−i1+i−1+i1−ii2−i2−22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ5122-2-22i−2i2i−2i00-102i−2i02-2−i3i3-111−i3i33−3−i−iii3−300002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23-113−3−i3i3−iiζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231+i−1−i1−i−1+ii2−i2−22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ5222-2-22i−2i2i−2i00-102i−2i02-2−i3i3-111−i3i33−3−i−iii3−300002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23-113−3−i3i3−iiζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−1−i1+i−1+i1−i−i2i22−2ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ5322-2-22i−2i2i−2i00-102i−2i02-2i3−i3-111i3−i3−33−i−iii−330000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23-11−33i3−i3−iiζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231+i−1−i1−i−1+i−i2i22−2−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ5422-2-22i−2i2i−2i00-102i−2i02-2i3−i3-111i3−i3−33−i−iii−330000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23-11−33i3−i3−iiζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−1−i1+i−1+i1−ii2−i2−22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ5522-2-22i−2i2i−2i00-102i−2i02-2i3−i3-111i3−i3−33−i−iii−3300002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23-11−33i3−i3−ii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231+i−1−i1−i−1+ii2−i2−22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ5622-2-22i−2i2i−2i00-102i−2i02-2i3−i3-111i3−i3−33−i−iii−3300002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23-11−33i3−i3−ii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−1−i1+i−1+i1−i−i2i22−2ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.