Finite Group Databasebeta

← Group #10693897

Character table — Group #10693897

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order122244442234444446666666121212121212121244888888881212121212121212242424242424242424242424242424248888888824242424242424242424242424242424888888888888
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
χ91111-1-1-1-1-1-11111-1-11-1-1-1-111111-1-1-1-1111-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−ii−i
χ101111-1-1-1-1-1-11111-1-11-1-1-1-111111-1-1-1-1111-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−ii
χ111111-1-1-1-1-1-11111-1-11-1-1-1-111111-1-1-1-1111-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−ii−ii
χ121111-1-1-1-1-1-11111-1-11-1-1-1-111111-1-1-1-1111-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−i−iii−i−iiii−ii−i
χ131111-1-1-1-1-1-11111-1-11-1-1-1-111111-1-1-1-1111-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiii−i−ii
χ141111-1-1-1-1-1-11111-1-11-1-1-1-111111-1-1-1-1111-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−iii−i
χ151111-1-1-1-1-1-11111-1-11-1-1-1-111111-1-1-1-1111-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−iii−i
χ161111-1-1-1-1-1-11111-1-11-1-1-1-111111-1-1-1-1111-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−ii−i−ii
χ17222222222222-2-2-2-22222222222222222-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000002-22-200000000
χ18222222222222-2-2-2-22222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-22-2200000000
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
χ2322222222-2-22-22222-2-2-2-2-2222-2-22222-2-2-2-222-2-222-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ2422222222-2-22-22222-2-2-2-2-2222-2-22222-2-2-2-2-2-222-2-222-2-222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ2522222222-2-22-2-2-2-2-2-2-2-2-2-2222-2-22222-2-2220000000022-2-222-2-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ2622222222-2-22-2-2-2-2-2-2-2-2-2-2222-2-22222-2-2220000000022-2-222-2-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ2722222222-2-2-1-22222-21111-1-1-111-1-1-1-111-2-222-2-222-2-211-1-111-1-1-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−3000000000000
χ2822222222-2-2-1-22222-21111-1-1-111-1-1-1-111-2-222-2-222-2-211-1-111-1-1-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−333000000000000
χ2922222222-2-2-1-22222-21111-1-1-111-1-1-1-111-2-2-2-222-2-22211-1-111-1-11111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−333000000000000
χ3022222222-2-2-1-22222-21111-1-1-111-1-1-1-111-2-2-2-222-2-22211-1-111-1-11111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−3000000000000
χ312222-2-2-2-2222-222-2-2-22222222-2-2-2-2-2-2-2-2-2222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ322222-2-2-2-2222-222-2-2-22222222-2-2-2-2-2-2-2-2-22-2-22222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000
χ332222-2-2-2-2222-2-2-222-22222222-2-2-2-2-2-2-2-22-2000000002222-2-2-2-2000000000000000000000000000000000000000000002-2-220000
χ342222-2-2-2-2222-2-2-222-22222222-2-2-2-2-2-2-2-22-2000000002222-2-2-2-200000000000000000000000000000000000000000000-222-20000
χ352222-2-2-2-222-1-222-2-2-2-1-1-1-1-1-1-111111111-2222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000033−3−3−3−33333−3−3−3−333000000000000
χ362222-2-2-2-222-1-222-2-2-2-1-1-1-1-1-1-111111111-2222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−3−33333−3−3−3−33333−3−3000000000000
χ372222-2-2-2-222-1-222-2-2-2-1-1-1-1-1-1-111111111-22-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−3000000000000
χ382222-2-2-2-222-1-222-2-2-2-1-1-1-1-1-1-111111111-22-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−333000000000000
χ392222-2-2-2-2-2-222-2-2222-2-2-2-222222-2-2-2-222-2200000000-2-22222-2-200000000000000000000000000000000000000002i−2i−2i2i00000000
χ402222-2-2-2-2-2-222-2-2222-2-2-2-222222-2-2-2-222-2200000000-2-22222-2-20000000000000000000000000000000000000000−2i2i2i−2i00000000
χ412222-2-2-2-2-2-2-1222-2-221111-1-1-1-1-11111-1-12-22222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-11111000000000000
χ422222-2-2-2-2-2-2-1222-2-221111-1-1-1-1-11111-1-12-22222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-1000000000000
χ432222-2-2-2-2-2-2-1222-2-221111-1-1-1-1-11111-1-12-2-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000
χ442222-2-2-2-2-2-2-1222-2-221111-1-1-1-1-11111-1-12-2-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000
χ4522-2-22i2i−2i−2i00202-22i−2i000002-2-2002i2i−2i−2i0000002i−2i002-2002i−2i002-200002i2i−2i−2i000022-2-22−2−i2i2−i2i22−22−22−2−i2i2−i2i2−i2i2−i2i22−22−2000000000000
χ4622-2-22i2i−2i−2i00202-22i−2i000002-2-2002i2i−2i−2i0000002i−2i002-2002i−2i002-200002i2i−2i−2i000022-2-2−22i2−i2i2−i2−22−22−22i2−i2i2−i2i2−i2i2−i2−22−22000000000000
χ4722-2-22i2i−2i−2i00202-22i−2i000002-2-2002i2i−2i−2i000000−2i2i00-22002i−2i002-20000−2i−2i2i2i0000-2-2222−2−i2i2i2−i2−222−22−2−i2i2−i2i2i2−i2i2−i2−22−22000000000000
χ4822-2-22i2i−2i−2i00202-22i−2i000002-2-2002i2i−2i−2i000000−2i2i00-22002i−2i002-20000−2i−2i2i2i0000-2-222−22i2−i2−i2i22−2−22−22i2−i2i2−i2−i2i2−i2i22−22−2000000000000
χ4922-2-22i2i−2i−2i00-102-22i−2i0−i3−i3i3i3-1113−3−i−iii3−300002i−2i002-23−3−ii−i3i3-11−i3−i3i3i3−i−iii33−3−3-1-1112−2−i2i2−i2i22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ5022-2-22i2i−2i−2i00-102-22i−2i0−i3−i3i3i3-1113−3−i−iii3−300002i−2i002-23−3−ii−i3i3-11−i3−i3i3i3−i−iii33−3−3-1-111−22i2−i2i2−i2−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ5122-2-22i2i−2i−2i00-102-22i−2i0−i3−i3i3i3-1113−3−i−iii3−30000−2i2i00-223−3−ii−i3i3-11i3i3−i3−i3ii−i−i−3−33311-1-12−2−i2i2i2−i2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ5222-2-22i2i−2i−2i00-102-22i−2i0−i3−i3i3i3-1113−3−i−iii3−30000−2i2i00-223−3−ii−i3i3-11i3i3−i3−i3ii−i−i−3−33311-1-1−22i2−i2−i2i22−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ5322-2-22i2i−2i−2i00-102-22i−2i0i3i3−i3−i3-111−33−i−iii−3300002i−2i002-2−33−iii3−i3-11i3i3−i3−i3−i−iii−3−333-1-1112−2−i2i2−i2i22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ5422-2-22i2i−2i−2i00-102-22i−2i0i3i3−i3−i3-111−33−i−iii−3300002i−2i002-2−33−iii3−i3-11i3i3−i3−i3−i−iii−3−333-1-111−22i2−i2i2−i2−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ5522-2-22i2i−2i−2i00-102-22i−2i0i3i3−i3−i3-111−33−i−iii−330000−2i2i00-22−33−iii3−i3-11−i3−i3i3i3ii−i−i33−3−311-1-12−2−i2i2i2−i2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ5622-2-22i2i−2i−2i00-102-22i−2i0i3i3−i3−i3-111−33−i−iii−330000−2i2i00-22−33−iii3−i3-11−i3−i3i3i3ii−i−i33−3−311-1-1−22i2−i2−i2i22−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ5722-2-2−2i−2i2i2i00202-2−2i2i000002-2-200−2i−2i2i2i0000002i−2i00-2200−2i2i002-200002i2i−2i−2i0000-2-2222−2i2−i2−i2i2−222−22−2i2−i2i2−i2−i2i2−i2i2−22−22000000000000
χ5822-2-2−2i−2i2i2i00202-2−2i2i000002-2-200−2i−2i2i2i0000002i−2i00-2200−2i2i002-200002i2i−2i−2i0000-2-222−22−i2i2i2−i22−2−22−22−i2i2−i2i2i2−i2i2−i22−22−2000000000000
χ5922-2-2−2i−2i2i2i00202-2−2i2i000002-2-200−2i−2i2i2i000000−2i2i002-200−2i2i002-20000−2i−2i2i2i000022-2-22−2i2−i2i2−i22−22−22−2i2−i2i2−i2i2−i2i2−i22−22−2000000000000
χ6022-2-2−2i−2i2i2i00202-2−2i2i000002-2-200−2i−2i2i2i000000−2i2i002-200−2i2i002-20000−2i−2i2i2i000022-2-2−22−i2i2−i2i2−22−22−22−i2i2−i2i2−i2i2−i2i2−22−22000000000000
χ6122-2-2−2i−2i2i2i00-102-2−2i2i0−i3−i3i3i3-111−33ii−i−i−3300002i−2i00-22−33i−i−i3i3-11i3i3−i3−i3−i−iii33−3−311-1-12−2i2−i2−i2i2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ6222-2-2−2i−2i2i2i00-102-2−2i2i0−i3−i3i3i3-111−33ii−i−i−3300002i−2i00-22−33i−i−i3i3-11i3i3−i3−i3−i−iii33−3−311-1-1−22−i2i2i2−i22−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ6322-2-2−2i−2i2i2i00-102-2−2i2i0−i3−i3i3i3-111−33ii−i−i−330000−2i2i002-2−33i−i−i3i3-11−i3−i3i3i3ii−i−i−3−333-1-1112−2i2−i2i2−i22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ6422-2-2−2i−2i2i2i00-102-2−2i2i0−i3−i3i3i3-111−33ii−i−i−330000−2i2i002-2−33i−i−i3i3-11−i3−i3i3i3ii−i−i−3−333-1-111−22−i2i2−i2i2−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ6522-2-2−2i−2i2i2i00-102-2−2i2i0i3i3−i3−i3-1113−3ii−i−i3−300002i−2i00-223−3i−ii3−i3-11−i3−i3i3i3−i−iii−3−33311-1-12−2i2−i2−i2i2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ6622-2-2−2i−2i2i2i00-102-2−2i2i0i3i3−i3−i3-1113−3ii−i−i3−300002i−2i00-223−3i−ii3−i3-11−i3−i3i3i3−i−iii−3−33311-1-1−22−i2i2i2−i22−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
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χ1014-4-44−4i4i4i−4i00-20000002i3−2i3−2i32i322-223−232i−2i−2i2i−23230022−22002i2−2i20000000000−222−26−6−66i2−i2−i2i2i6−i6−i6i6000000000000000000000000000000000000
χ1024-4-44−4i4i4i−4i00-20000002i3−2i3−2i32i322-223−232i−2i−2i2i−232300−222200−2i22i200000000002−2−22−666−6−i2i2i2−i2−i6i6i6−i6000000000000000000000000000000000000

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