Finite Group Databasebeta

← Group #11714755

Character table — Group #11714755

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size11112222223333666666888888888888888824242424242424241111222222333366666688888888888888882424242424242424
order1244248888224424888836661212121224242424242424242244444422442488882244248888666612121212242424242424242422444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-1111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-1
χ4111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ511-1-1-1111-1-111-1-1-1111-1-11-1-11-1-1111111-1-1-1-111-1-11-11-111-1-1-1111-1-111-1-1-1111-1-11-1-11-1-1111111-1-1-1-111-1-11-11-1
χ611-1-1-1111-1-111-1-1-1111-1-11-1-11-1-1111111-1-1-1-1-1-111-11-1111-1-1-1111-1-111-1-1-1111-1-11-1-11-1-1111111-1-1-1-1-1-111-11-11
χ711-1-1-11-1-11111-1-1-11-1-1111-1-11-1-111-1-1-1-111111-1-111-1-1111-1-1-11-1-11111-1-1-11-1-1111-1-11-1-111-1-1-1-111111-1-111-1-11
χ811-1-1-11-1-11111-1-1-11-1-1111-1-11-1-111-1-1-1-11111-111-1-111-111-1-1-11-1-11111-1-1-11-1-1111-1-11-1-111-1-1-1-11111-111-1-111-1
χ922222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ10222222-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000222222-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000
χ112222-2-200002222-2-200002-2-2222-2-200000000000000002222-2-200002222-2-200002-2-2222-2-20000000000000000
χ122222-2-200002222-2-20000-111-1-1-11133−3−333−3−3000000002222-2-200002222-2-20000-111-1-1-11133−3−333−3−300000000
χ132222-2-200002222-2-20000-111-1-1-111−3−333−3−333000000002222-2-200002222-2-20000-111-1-1-111−3−333−3−33300000000
χ1422-2-22-2000022-2-22-200002222-2-2-2-2000000000000000022-2-22-2000022-2-22-200002222-2-2-2-20000000000000000
χ1522-2-22-2000022-2-22-20000-1-1-1-1111133−3−3−3−3330000000022-2-22-2000022-2-22-20000-1-1-1-1111133−3−3−3−33300000000
χ1622-2-22-2000022-2-22-20000-1-1-1-11111−3−33333−3−30000000022-2-22-2000022-2-22-20000-1-1-1-11111−3−33333−3−300000000
χ1722-2-2-2222-2-222-2-2-2222-2-2-111-111-1-1-1-1-1-111110000000022-2-2-2222-2-222-2-2-2222-2-2-111-111-1-1-1-1-1-1111100000000
χ1822-2-2-22-2-22222-2-2-22-2-222-111-111-1-11111-1-1-1-10000000022-2-2-22-2-22222-2-2-22-2-222-111-111-1-11111-1-1-1-100000000
χ192-22i−2i002−2−i2i22-22i−2i002−2−i2i2200-22i−2i002−22−2−i2i2−i2i2000000002-22i−2i002−2−i2i22-22i−2i002−2−i2i2200-22i−2i002−22−2−i2i2−i2i200000000
χ202-22i−2i002−2−i2i22-22i−2i002−2−i2i2-1−i3i31−ii3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000002-22i−2i002−2−i2i22-22i−2i002−2−i2i2-1−i3i31−ii3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ212-22i−2i002−2−i2i22-22i−2i002−2−i2i2-1i3−i31−ii−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000002-22i−2i002−2−i2i22-22i−2i002−2−i2i2-1i3−i31−ii−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ222-22i−2i00−22i2−i22-22i−2i00−22i2−i2200-22i−2i00−22−22i2−i2i2−i2000000002-22i−2i00−22i2−i22-22i−2i00−22i2−i2200-22i−2i00−22−22i2−i2i2−i200000000
χ232-22i−2i00−22i2−i22-22i−2i00−22i2−i2-1−i3i31−ii3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000002-22i−2i00−22i2−i22-22i−2i00−22i2−i2-1−i3i31−ii3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ242-22i−2i00−22i2−i22-22i−2i00−22i2−i2-1i3−i31−ii−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000002-22i−2i00−22i2−i22-22i−2i00−22i2−i2-1i3−i31−ii−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ252-2−2i2i002−2i2−i22-2−2i2i002−2i2−i2200-2−2i2i002−22−2i2−i2i2−i2000000002-2−2i2i002−2i2−i22-2−2i2i002−2i2−i2200-2−2i2i002−22−2i2−i2i2−i200000000
χ262-2−2i2i002−2i2−i22-2−2i2i002−2i2−i2-1−i3i31i−i−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000002-2−2i2i002−2i2−i22-2−2i2i002−2i2−i2-1−i3i31i−i−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ272-2−2i2i002−2i2−i22-2−2i2i002−2i2−i2-1i3−i31i−i3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000002-2−2i2i002−2i2−i22-2−2i2i002−2i2−i2-1i3−i31i−i3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ282-2−2i2i00−22−i2i22-2−2i2i00−22−i2i2200-2−2i2i00−22−22−i2i2−i2i2000000002-2−2i2i00−22−i2i22-2−2i2i00−22−i2i2200-2−2i2i00−22−22−i2i2−i2i200000000
χ292-2−2i2i00−22−i2i22-2−2i2i00−22−i2i2-1−i3i31i−i−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000002-2−2i2i00−22−i2i22-2−2i2i00−22−i2i2-1−i3i31i−i−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ302-2−2i2i00−22−i2i22-2−2i2i00−22−i2i2-1i3−i31i−i3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000002-2−2i2i00−22−i2i22-2−2i2i00−22−i2i2-1i3−i31i−i3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ313333333333-1-1-1-1-1-1-1-1-1-100000000000000001111-1-1-1-13333333333-1-1-1-1-1-1-1-1-1-100000000000000001111-1-1-1-1
χ323333333333-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-111113333333333-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-11111
χ33333333-3-3-3-3-1-1-1-1-1-1111100000000000000001-11-1-1-111333333-3-3-3-3-1-1-1-1-1-1111100000000000000001-11-1-1-111
χ34333333-3-3-3-3-1-1-1-1-1-111110000000000000000-11-1111-1-1333333-3-3-3-3-1-1-1-1-1-111110000000000000000-11-1111-1-1
χ3533-3-3-3333-3-3-1-1111-1-1-111000000000000000011-1-1-11-1133-3-3-3333-3-3-1-1111-1-1-111000000000000000011-1-1-11-11
χ3633-3-3-3333-3-3-1-1111-1-1-1110000000000000000-1-1111-11-133-3-3-3333-3-3-1-1111-1-1-1110000000000000000-1-1111-11-1
χ3733-3-3-33-3-333-1-1111-111-1-100000000000000001-1-11-111-133-3-3-33-3-333-1-1111-111-1-100000000000000001-1-11-111-1
χ3833-3-3-33-3-333-1-1111-111-1-10000000000000000-111-11-1-1133-3-3-33-3-333-1-1111-111-1-10000000000000000-111-11-1-11
χ396666-6-60000-2-2-2-22200000000000000000000000000006666-6-60000-2-2-2-2220000000000000000000000000000
χ4066-6-66-60000-2-222-22000000000000000000000000000066-6-66-60000-2-222-220000000000000000000000000000
χ416-66i−6i0032−32−3i23i2-22−2i2i00−22i2−i20000000000000000000000006-66i−6i0032−32−3i23i2-22−2i2i00−22i2−i2000000000000000000000000
χ426-66i−6i00−32323i2−3i2-22−2i2i002−2−i2i20000000000000000000000006-66i−6i00−32323i2−3i2-22−2i2i002−2−i2i2000000000000000000000000
χ436-6−6i6i0032−323i2−3i2-222i−2i00−22−i2i20000000000000000000000006-6−6i6i0032−323i2−3i2-222i−2i00−22−i2i2000000000000000000000000
χ446-6−6i6i00−3232−3i23i2-222i−2i002−2i2−i20000000000000000000000006-6−6i6i00−3232−3i23i2-222i−2i002−2i2−i2000000000000000000000000
χ4511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ46111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ47111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-11-1-111
χ48111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-111-1-1
χ4911-1-1-1111-1-111-1-1-1111-1-11-1-11-1-1111111-1-1-1-111-1-11-11-1-1-1111-1-1-111-1-1111-1-1-111-111-111-1-1-1-1-1-11111-1-111-11-11
χ5011-1-1-1111-1-111-1-1-1111-1-11-1-11-1-1111111-1-1-1-1-1-111-11-11-1-1111-1-1-111-1-1111-1-1-111-111-111-1-1-1-1-1-1111111-1-11-11-1
χ5111-1-1-11-1-11111-1-1-11-1-1111-1-11-1-111-1-1-1-111111-1-111-1-11-1-1111-111-1-1-1-1111-111-1-1-111-111-1-11111-1-1-1-1-111-1-111-1
χ5211-1-1-11-1-11111-1-1-11-1-1111-1-11-1-111-1-1-1-11111-111-1-111-1-1-1111-111-1-1-1-1111-111-1-1-111-111-1-11111-1-1-1-11-1-111-1-11
χ5322222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111111100000000
χ54222222-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000-2-2-2-2-2-22222-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000
χ552222-2-200002222-2-200002-2-2222-2-20000000000000000-2-2-2-2220000-2-2-2-2220000-222-2-2-2220000000000000000
χ562222-2-200002222-2-20000-111-1-1-11133−3−333−3−300000000-2-2-2-2220000-2-2-2-22200001-1-1111-1-1−3−333−3−33300000000
χ572222-2-200002222-2-20000-111-1-1-111−3−333−3−33300000000-2-2-2-2220000-2-2-2-22200001-1-1111-1-133−3−333−3−300000000
χ5822-2-22-2000022-2-22-200002222-2-2-2-20000000000000000-2-222-220000-2-222-220000-2-2-2-222220000000000000000
χ5922-2-22-2000022-2-22-20000-1-1-1-1111133−3−3−3−33300000000-2-222-220000-2-222-2200001111-1-1-1-1−3−33333−3−300000000
χ6022-2-22-2000022-2-22-20000-1-1-1-11111−3−33333−3−300000000-2-222-220000-2-222-2200001111-1-1-1-133−3−3−3−33300000000
χ6122-2-2-2222-2-222-2-2-2222-2-2-111-111-1-1-1-1-1-1111100000000-2-2222-2-2-222-2-2222-2-2-2221-1-11-1-1111111-1-1-1-100000000
χ6222-2-2-22-2-22222-2-2-22-2-222-111-111-1-11111-1-1-1-100000000-2-2222-222-2-2-2-2222-222-2-21-1-11-1-111-1-1-1-1111100000000
χ632-22i−2i002−2−i2i22-22i−2i002−2−i2i2200-22i−2i002−22−2−i2i2−i2i200000000-22−2i2i00−22i2−i2-22−2i2i00−22i2−i2-2002−2i2i00−22−22i2−i2i2−i200000000
χ642-22i−2i002−2−i2i22-22i−2i002−2−i2i2-1−i3i31−ii3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000-22−2i2i00−22i2−i2-22−2i2i00−22i2−i21i3−i3-1i−i−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ652-22i−2i002−2−i2i22-22i−2i002−2−i2i2-1i3−i31−ii−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000-22−2i2i00−22i2−i2-22−2i2i00−22i2−i21−i3i3-1i−i3−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ662-22i−2i00−22i2−i22-22i−2i00−22i2−i2200-22i−2i00−22−22i2−i2i2−i200000000-22−2i2i002−2−i2i2-22−2i2i002−2−i2i2-2002−2i2i002−22−2−i2i2−i2i200000000
χ672-22i−2i00−22i2−i22-22i−2i00−22i2−i2-1−i3i31−ii3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000-22−2i2i002−2−i2i2-22−2i2i002−2−i2i21i3−i3-1i−i−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ682-22i−2i00−22i2−i22-22i−2i00−22i2−i2-1i3−i31−ii−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000-22−2i2i002−2−i2i2-22−2i2i002−2−i2i21−i3i3-1i−i3−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ692-2−2i2i002−2i2−i22-2−2i2i002−2i2−i2200-2−2i2i002−22−2i2−i2i2−i200000000-222i−2i00−22−i2i2-222i−2i00−22−i2i2-20022i−2i00−22−22−i2i2−i2i200000000
χ702-2−2i2i002−2i2−i22-2−2i2i002−2i2−i2-1−i3i31i−i−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000-222i−2i00−22−i2i2-222i−2i00−22−i2i21i3−i3-1−ii3−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ712-2−2i2i002−2i2−i22-2−2i2i002−2i2−i2-1i3−i31i−i3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000-222i−2i00−22−i2i2-222i−2i00−22−i2i21−i3i3-1−ii−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ722-2−2i2i00−22−i2i22-2−2i2i00−22−i2i2200-2−2i2i00−22−22−i2i2−i2i200000000-222i−2i002−2i2−i2-222i−2i002−2i2−i2-20022i−2i002−22−2i2−i2i2−i200000000
χ732-2−2i2i00−22−i2i22-2−2i2i00−22−i2i2-1−i3i31i−i−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000-222i−2i002−2i2−i2-222i−2i002−2i2−i21i3−i3-1−ii3−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ742-2−2i2i00−22−i2i22-2−2i2i00−22−i2i2-1i3−i31i−i3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000-222i−2i002−2i2−i2-222i−2i002−2i2−i21−i3i3-1−ii−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ753333333333-1-1-1-1-1-1-1-1-1-100000000000000001111-1-1-1-1-3-3-3-3-3-3-3-3-3-311111111110000000000000000-1-1-1-11111
χ763333333333-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-11111-3-3-3-3-3-3-3-3-3-3111111111100000000000000001111-1-1-1-1
χ77333333-3-3-3-3-1-1-1-1-1-1111100000000000000001-11-1-1-111-3-3-3-3-3-33333111111-1-1-1-10000000000000000-11-1111-1-1
χ78333333-3-3-3-3-1-1-1-1-1-111110000000000000000-11-1111-1-1-3-3-3-3-3-33333111111-1-1-1-100000000000000001-11-1-1-111
χ7933-3-3-3333-3-3-1-1111-1-1-111000000000000000011-1-1-11-11-3-3333-3-3-33311-1-1-1111-1-10000000000000000-1-1111-11-1
χ8033-3-3-3333-3-3-1-1111-1-1-1110000000000000000-1-1111-11-1-3-3333-3-3-33311-1-1-1111-1-1000000000000000011-1-1-11-11
χ8133-3-3-33-3-333-1-1111-111-1-100000000000000001-1-11-111-1-3-3333-333-3-311-1-1-11-1-1110000000000000000-111-11-1-11
χ8233-3-3-33-3-333-1-1111-111-1-10000000000000000-111-11-1-11-3-3333-333-3-311-1-1-11-1-11100000000000000001-1-11-111-1
χ836666-6-60000-2-2-2-2220000000000000000000000000000-6-6-6-66600002222-2-20000000000000000000000000000
χ8466-6-66-60000-2-222-220000000000000000000000000000-6-666-66000022-2-22-20000000000000000000000000000
χ856-66i−6i0032−32−3i23i2-22−2i2i00−22i2−i2000000000000000000000000-66−6i6i00−32323i2−3i22-22i−2i002−2−i2i2000000000000000000000000
χ866-66i−6i00−32323i2−3i2-22−2i2i002−2−i2i2000000000000000000000000-66−6i6i0032−32−3i23i22-22i−2i00−22i2−i2000000000000000000000000
χ876-6−6i6i0032−323i2−3i2-222i−2i00−22−i2i2000000000000000000000000-666i−6i00−3232−3i23i22-2−2i2i002−2i2−i2000000000000000000000000
χ886-6−6i6i00−3232−3i23i2-222i−2i002−2i2−i2000000000000000000000000-666i−6i0032−323i2−3i22-2−2i2i00−22−i2i2000000000000000000000000

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