Finite Group Databasebeta

← Group #10696032

Character table — Group #10696032

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444444444888888888888888888888888881616161616162424242424242424242424244848
order12224444223446661212121244446612121212121222446666888812121212121224242424242424242466121244444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ922222222222222222222-2-2-2-222-2-222-2-2000000000000-2-2000000000000000000000022-2-2000000
χ1022222222222222222222-2-2-2-222-2-222-2-2000000000000-2-20000000000000000000000-2-222000000
χ112222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000
χ122222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111-2-2111100000000000000
χ132222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-1-2-2111100000000000000
χ142222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-111111111111122-1-1-1-100000000000000
χ1522222222-2-22-2-222222222-22-2-2-222-2-2220000000022-2-2-2-200002222-2-2-2-200000000000000000000
χ1622222222-2-22-2-222222222-22-2-2-222-2-22200000000-2-222-2-20000-2-2-2-2222200000000000000000000
χ1722222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-2000000000000220000000000000000000000000022-2-200
χ1822222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-20000000000002200000000000000000000000000-2-22200
χ1922222222-2-2-1-2-2-1-1-1-1-1-1-12-22-211-1-111-1-10000−i3−i3i3i322-2-211−i3−i3i3i3-1-1-1-1111100−i3i3−i3i300000000000000
χ2022222222-2-2-1-2-2-1-1-1-1-1-1-12-22-211-1-111-1-10000−i3−i3i3i3-2-22211−i3−i3i3i31111-1-1-1-100i3−i3i3−i300000000000000
χ2122222222-2-2-1-2-2-1-1-1-1-1-1-12-22-211-1-111-1-10000i3i3−i3−i322-2-211i3i3−i3−i3-1-1-1-1111100i3−i3i3−i300000000000000
χ2222222222-2-2-1-2-2-1-1-1-1-1-1-12-22-211-1-111-1-10000i3i3−i3−i3-2-22211i3i3−i3−i31111-1-1-1-100−i3i3−i3i300000000000000
χ232222-2-2-2-2222-2-2222-2-2-2-22-2-222222-2-2-2-20000000000002-200000000000000000022-2-20000000000
χ242222-2-2-2-2222-2-2222-2-2-2-22-2-222222-2-2-2-20000000000002-2000000000000000000-2-2220000000000
χ252222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-2-2-22222-2-222220000-22-2-2-2-20000000000000000000000000000
χ262222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-2-2-222-2-222-2-2-2-20000-2222220000000000000000000000000000
χ272222-2-2-2-222-1-2-2-1-1-11111-222-2-1-11111-1-122-2-2-1-1-1-100001-11111−i3−i3i3i3−i3−i3i3i300−i3i3i3−i300000000000000
χ282222-2-2-2-222-1-2-2-1-1-11111-222-2-1-11111-1-122-2-2-1-1-1-100001-11111i3i3−i3−i3i3i3−i3−i300i3−i3−i3i300000000000000
χ292222-2-2-2-222-1-2-2-1-1-11111-222-2-1-11111-1-1-2-222111100001-1-1-1-1-1−i3−i3i3i3−i3−i3i3i300i3−i3−i3i300000000000000
χ302222-2-2-2-222-1-2-2-1-1-11111-222-2-1-11111-1-1-2-222111100001-1-1-1-1-1i3i3−i3−i3i3i3−i3−i300−i3i3i3−i300000000000000
χ312222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-2000000000000-220000000000000000000000000000002i−2i
χ322222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-2000000000000-22000000000000000000000000000000−2i2i
χ332222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-222220000000000002-20000000000002-222-2-200000000000000
χ342222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-222220000000000002-2000000000000-22-2-22200000000000000
χ352222-2-2-2-2-2-2-122-1-1-11111-2-2221111-1-1-1-10000−i3−i3i3i30000-11i3i3−i3−i3−i3−i3i3i3i3i3−i3−i32-2-1-11100000000000000
χ362222-2-2-2-2-2-2-122-1-1-11111-2-2221111-1-1-1-10000−i3−i3i3i30000-11i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-2211-1-100000000000000
χ372222-2-2-2-2-2-2-122-1-1-11111-2-2221111-1-1-1-10000i3i3−i3−i30000-11−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-2211-1-100000000000000
χ382222-2-2-2-2-2-2-122-1-1-11111-2-2221111-1-1-1-10000i3i3−i3−i30000-11−i3−i3i3i3i3i3−i3−i3−i3−i3i3i32-2-1-11100000000000000
χ3922-2-222-2-22-222-2-2-2222-2-200002-2002-200000000002−22−20000002−22−22−22−20000000000002i−2i−i2i2−i2i200
χ4022-2-222-2-22-222-2-2-2222-2-200002-2002-200000000002−22−20000002−22−22−22−2000000000000−2i2ii2−i2i2−i200
χ4122-2-222-2-22-222-2-2-2222-2-200002-2002-20000000000−22−22000000−22−22−22−220000000000002i−2ii2−i2i2−i200
χ4222-2-222-2-22-222-2-2-2222-2-200002-2002-20000000000−22−22000000−22−22−22−22000000000000−2i2i−i2i2−i2i200
χ4322-2-222-2-2-222-22-2-2222-2-20000-2200-2200000000002−2−220000002−22−2−22−2200000000002i−2i00−i2i2i2−i200
χ4422-2-222-2-2-222-22-2-2222-2-20000-2200-2200000000002−2−220000002−22−2−22−220000000000−2i2i00i2−i2−i2i200
χ4522-2-222-2-2-222-22-2-2222-2-20000-2200-220000000000−222−2000000−22−222−22−200000000002i−2i00i2−i2−i2i200
χ4622-2-222-2-2-222-22-2-2222-2-20000-2200-220000000000−222−2000000−22−222−22−20000000000−2i2i00−i2i2i2−i200
χ474444444444-244-2-2-2-2-2-2-2-4-4-4-4-2-222-2-2220000000000002200000000000000000000000000000000
χ4844444444-4-4-2-4-4-2-2-2-2-2-2-2-44-4422222222000000000000-2-200000000000000000000000000000000
χ494444-4-4-4-444-2-4-4-2-2-222224-4-44-2-2-2-22222000000000000-2200000000000000000000000000000000
χ504444-4-4-4-4-4-4-244-2-2-2222244-4-422-2-2-2-2220000000000002-200000000000000000000000000000000
χ5144-4-444-4-44-4-24-422-2-2-2220000-2200-22000000000022−2222−22000000−22−22−22−2200000000000000000000
χ5244-4-444-4-44-4-24-422-2-2-2220000-2200-220000000000−2222−22220000002−22−22−22−200000000000000000000
χ5344-4-444-4-4-44-2-4422-2-2-22200002-2002-2000000000022−22−2222000000−22−222−22−200000000000000000000
χ5444-4-444-4-4-44-2-4422-2-2-22200002-2002-20000000000−222222−220000002−22−2−22−2200000000000000000000
χ5544-4-4-4-4444-44-44-4-44-4-44400004-400-44000000000000000000000000000000000000000000000000
χ5644-4-4-4-4444-4-2-4422-222-2-20000-22002-200000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000
χ5744-4-4-4-4444-4-2-4422-222-2-20000-22002-200000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000
χ5844-4-4-4-444-4444-4-4-44-4-4440000-44004-4000000000000000000000000000000000000000000000000
χ5944-4-4-4-444-44-24-422-222-2-200002-200-2200000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000
χ6044-4-4-4-444-44-24-422-222-2-200002-200-2200000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000
χ614-44-44i−4i4i−4i004004-4-44i−4i4i−4i000000000000000000000000000000000000000000002-22i−2i0000000000
χ624-44-44i−4i4i−4i004004-4-44i−4i4i−4i00000000000000000000000000000000000000000000-22−2i2i0000000000
χ634-44-4−4i4i−4i4i004004-4-4−4i4i−4i4i000000000000000000000000000000000000000000002-2−2i2i0000000000
χ644-44-4−4i4i−4i4i004004-4-4−4i4i−4i4i00000000000000000000000000000000000000000000-222i−2i0000000000
χ654-4-444i−4i−4i4i00400-44-44i−4i−4i4i0000000000002-22i−2i2-22-20000002i−2i2i−2i0000000000000000000000000000
χ664-4-444i−4i−4i4i00400-44-44i−4i−4i4i000000000000-22−2i2i-22-22000000−2i2i−2i2i0000000000000000000000000000
χ674-4-444i−4i−4i4i00-2002-22−2i2i2i−2i00000023−2300−2i32i32-22i−2i−1−i31+i3−1+i31−i30000002ζ22−2ζ222ζ14−2ζ140000000000000000000000000000
χ684-4-444i−4i−4i4i00-2002-22−2i2i2i−2i00000023−2300−2i32i3-22−2i2i1+i3−1−i31−i3−1+i3000000−2ζ222ζ22−2ζ142ζ140000000000000000000000000000
χ694-4-444i−4i−4i4i00-2002-22−2i2i2i−2i000000−2323002i3−2i32-22i−2i−1+i31−i3−1−i31+i30000002ζ14−2ζ142ζ22−2ζ220000000000000000000000000000
χ704-4-444i−4i−4i4i00-2002-22−2i2i2i−2i000000−2323002i3−2i3-22−2i2i1−i3−1+i31+i3−1−i3000000−2ζ142ζ14−2ζ222ζ220000000000000000000000000000
χ714-4-44−4i4i4i−4i00400-44-4−4i4i4i−4i0000000000002-2−2i2i2-22-2000000−2i2i−2i2i0000000000000000000000000000
χ724-4-44−4i4i4i−4i00400-44-4−4i4i4i−4i000000000000-222i−2i-22-220000002i−2i2i−2i0000000000000000000000000000
χ734-4-44−4i4i4i−4i00-2002-222i−2i−2i2i00000023−23002i3−2i32-2−2i2i−1+i31−i3−1−i31+i3000000−2ζ142ζ14−2ζ222ζ220000000000000000000000000000
χ744-4-44−4i4i4i−4i00-2002-222i−2i−2i2i00000023−23002i3−2i3-222i−2i1−i3−1+i31+i3−1−i30000002ζ14−2ζ142ζ22−2ζ220000000000000000000000000000
χ754-4-44−4i4i4i−4i00-2002-222i−2i−2i2i000000−232300−2i32i32-2−2i2i−1−i31+i3−1+i31−i3000000−2ζ222ζ22−2ζ142ζ140000000000000000000000000000
χ764-4-44−4i4i4i−4i00-2002-222i−2i−2i2i000000−232300−2i32i3-222i−2i1+i3−1−i31−i3−1+i30000002ζ22−2ζ222ζ14−2ζ140000000000000000000000000000
χ778-88-88i−8i8i−8i00-400-444−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ788-88-8−8i8i−8i8i00-400-4444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000

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