Finite Group Databasebeta

← Group #10691311

Character table — Group #10691311

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order12224444344444444666121212121212121212121212246688888888121212121212242424242424242424242424242424248888888824242424242424242424242424242424244488882488
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-1iiii−i−i−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-1iiii−i−i−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-11−ii
χ111111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-1iiii−i−i−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ121111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-1iiii−i−i−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-1-111−i−iii1-1i−i
χ131111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-1−i−i−i−iiiii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ141111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-1−i−i−i−iiiii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-11i−i
χ151111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-1−i−i−i−iiiii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11-1-1−i−i−i−iiiii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i1-1−ii
χ1722222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ1822222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ19222222222-2-22222-2-2222222222222222-2-2-2-200000000-2-2-2-2-2-200000000000000000000000000000000000000002-2-2200000000
χ20222222222-2-22222-2-2222222222222222-2-2-2-200000000-2-2-2-2-2-20000000000000000000000000000000000000000-222-200000000
χ21222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-222-2-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ22222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-222-2-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-21122-2-222-2-2-1-111-1-1-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−3000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-21122-2-222-2-2-1-111-1-1-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−333000000000000
χ2922222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-211-2-222-2-222-1-111-1-11111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−333000000000000
χ3022222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-211-2-222-2-222-1-111-1-11111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−3000000000000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-2-2-2-2-222222-2222i2i−2i−2i−2i−2i2i2i22-2-2-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-2-2-2-2-222222-222−2i−2i2i2i2i2i−2i−2i22-2-2-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ332222-2-2-2-22-2-222-2-222222-2-2-2-22222-2-2-2-22-22200000000-2-2-2-22200000000000000000000000000000000000000002-22-200000000
χ342222-2-2-2-22-2-222-2-222222-2-2-2-22222-2-2-2-22-22200000000-2-2-2-2220000000000000000000000000000000000000000-22-2200000000
χ352222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22222-22-2-200000000-2-22222000000000000000000000000000000000000000000002-2-220000
χ362222-2-2-2-22-2-2-2-22222222-2-2-2-2-2-2-2-22222-22-2-200000000-2-2222200000000000000000000000000000000000000000000-222-20000
χ372222-2-2-2-2-12222-2-2-2-2-1-1-11111-1-1-1-11111-22112i2i2i2i−2i−2i−2i−2i-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii000000000000
χ382222-2-2-2-2-12222-2-2-2-2-1-1-11111-1-1-1-11111-22112i2i2i2i−2i−2i−2i−2i-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i000000000000
χ392222-2-2-2-2-12222-2-2-2-2-1-1-11111-1-1-1-11111-2211−2i−2i−2i−2i2i2i2i2i-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i000000000000
χ402222-2-2-2-2-12222-2-2-2-2-1-1-11111-1-1-1-11111-2211−2i−2i−2i−2i2i2i2i2i-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000
χ412222-2-2-2-2-122-2-222-2-2-1-1-111111111-1-1-1-12-2-1-12i2i−2i−2i−2i−2i2i2i-1-11111−i−i−i−iiiiiiiii−i−i−i−i0000000033−3−3−3−333i3i3−i3−i3−i3−i3i3i3000000000000
χ422222-2-2-2-2-122-2-222-2-2-1-1-111111111-1-1-1-12-2-1-12i2i−2i−2i−2i−2i2i2i-1-11111−i−i−i−iiiiiiiii−i−i−i−i00000000−3−33333−3−3−i3−i3i3i3i3i3−i3−i3000000000000
χ432222-2-2-2-2-122-2-222-2-2-1-1-111111111-1-1-1-12-2-1-1−2i−2i2i2i2i2i−2i−2i-1-11111iiii−i−i−i−i−i−i−i−iiiii0000000033−3−3−3−333−i3−i3i3i3i3i3−i3−i3000000000000
χ442222-2-2-2-2-122-2-222-2-2-1-1-111111111-1-1-1-12-2-1-1−2i−2i2i2i2i2i−2i−2i-1-11111iiii−i−i−i−i−i−i−i−iiiii00000000−3−33333−3−3i3i3−i3−i3−i3−i3i3i3000000000000
χ4522-2-22i−2i2i−2i22-200002i−2i2-2-22i2i−2i−2i00000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232-2002i−2i0000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232−2−i2i21−i−1+i1+i−1−i2−22−2−i2i2−i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4622-2-22i−2i2i−2i22-200002i−2i2-2-22i2i−2i−2i00000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232-2002i−2i0000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−22i2−i2−1+i1−i−1−i1+i−22−22i2−i2i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4722-2-22i−2i2i−2i22-200002i−2i2-2-22i2i−2i−2i000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232-2002i−2i00002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232−2−i2i2−1+i1−i−1−i1+i2−22−2−i2i2−i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4822-2-22i−2i2i−2i22-200002i−2i2-2-22i2i−2i−2i000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232-2002i−2i00002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−22i2−i21−i−1+i1+i−1−i−22−22i2−i2i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4922-2-22i−2i2i−2i-12-200002i−2i-111−i−iii33−3−3−i3−i3i3i300−i3i300−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23-113−3−ii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ232−2−i2i21−i−1+i1+i−1−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000000000
χ5022-2-22i−2i2i−2i-12-200002i−2i-111−i−iii33−3−3−i3−i3i3i300−i3i300−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23-113−3−ii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−22i2−i2−1+i1−i−1−i1+i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000000000
χ5122-2-22i−2i2i−2i-12-200002i−2i-111−i−iii33−3−3−i3−i3i3i300−i3i3002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23-113−3−iiζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ232−2−i2i2−1+i1−i−1−i1+iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000000000
χ5222-2-22i−2i2i−2i-12-200002i−2i-111−i−iii33−3−3−i3−i3i3i300−i3i3002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23-113−3−iiζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−22i2−i21−i−1+i1+i−1−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000000000
χ5322-2-22i−2i2i−2i-12-200002i−2i-111−i−iii−3−333i3i3−i3−i300i3−i300−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23-11−33−iiζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ232−2−i2i21−i−1+i1+i−1−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000000000
χ5422-2-22i−2i2i−2i-12-200002i−2i-111−i−iii−3−333i3i3−i3−i300i3−i300−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23-11−33−iiζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−22i2−i2−1+i1−i−1−i1+i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000000000
χ5522-2-22i−2i2i−2i-12-200002i−2i-111−i−iii−3−333i3i3−i3−i300i3−i3002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23-11−33−ii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ232−2−i2i2−1+i1−i−1−i1+iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000000000
χ5622-2-22i−2i2i−2i-12-200002i−2i-111−i−iii−3−333i3i3−i3−i300i3−i3002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23-11−33−ii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−22i2−i21−i−1+i1+i−1−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.