Finite Group Databasebeta

← Group #10696048

Character table — Group #10696048

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444444444888888888888888888888888881616161616162424242424242424242424244848
order12224444223446661212121244446612121212121244448888121212121212121212122424242424242424441212121222444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ922222222222222222222-2-2-2-22222-2-2-2-200000000-2-20000000000000000000000000022-2-2000000
χ1022222222222222222222-2-2-2-22222-2-2-2-200000000-2-200000000000000000000000000-2-222000000
χ112222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000
χ122222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2111100000000000000
χ132222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-2111100000000000000
χ142222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-100000000000000
χ1522222222-2-22-2-222222222-22-2-2-2-2-22222000022-2-2-2-2000000002222-2-2-2-200000000000000000000
χ1622222222-2-22-2-222222222-22-2-2-2-2-222220000-2-222-2-200000000-2-2-2-2222200000000000000000000
χ1722222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-2000000002200000000000000000000000000000022-2-200
χ1822222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-20000000022000000000000000000000000000000-2-22200
χ1922222222-2-2-1-2-2-1-1-1-1-1-1-12-22-21111-1-1-1-1000022-2-211−i3−i3−i3−i3i3i3i3i3-1-1-1-1111100−i3−i3i3i300000000000000
χ2022222222-2-2-1-2-2-1-1-1-1-1-1-12-22-21111-1-1-1-1000022-2-211i3i3i3i3−i3−i3−i3−i3-1-1-1-1111100i3i3−i3−i300000000000000
χ2122222222-2-2-1-2-2-1-1-1-1-1-1-12-22-21111-1-1-1-10000-2-22211−i3−i3−i3−i3i3i3i3i31111-1-1-1-100i3i3−i3−i300000000000000
χ2222222222-2-2-1-2-2-1-1-1-1-1-1-12-22-21111-1-1-1-10000-2-22211i3i3i3i3−i3−i3−i3−i31111-1-1-1-100−i3−i3i3i300000000000000
χ232222-2-2-2-2222-2-2222-2-2-2-22-2-2222-2-222-2-2000000002-2000000000000000000000022-2-20000000000
χ242222-2-2-2-2222-2-2222-2-2-2-22-2-2222-2-222-2-2000000002-20000000000000000000000-2-2220000000000
χ252222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-2-2-22222-2-20000-2222-2-222-2-20000000000000000000000000000
χ262222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-2-2-222-2-2220000-22-2-222-2-2220000000000000000000000000000
χ272222-2-2-2-222-1-2-2-1-1-11111-222-2-1-11111-1-122-2-200001-1-1-111-1-111−i3−i3i3i3−i3−i3i3i300−i3i3−i3i300000000000000
χ282222-2-2-2-222-1-2-2-1-1-11111-222-2-1-11111-1-122-2-200001-1-1-111-1-111i3i3−i3−i3i3i3−i3−i300i3−i3i3−i300000000000000
χ292222-2-2-2-222-1-2-2-1-1-11111-222-2-1-11111-1-1-2-22200001-111-1-111-1-1−i3−i3i3i3−i3−i3i3i300i3−i3i3−i300000000000000
χ302222-2-2-2-222-1-2-2-1-1-11111-222-2-1-11111-1-1-2-22200001-111-1-111-1-1i3i3−i3−i3i3i3−i3−i300−i3i3−i3i300000000000000
χ312222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-200000000-2200000000000000000000000000000000002i−2i
χ322222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-200000000-220000000000000000000000000000000000−2i2i
χ332222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-222-2-222000000002-200000000000000002-22-2-2200000000000000
χ342222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-222-2-222000000002-20000000000000000-22-222-200000000000000
χ352222-2-2-2-2-2-2-122-1-1-11111-2-22211-1-111-1-100000000-11−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i32-2-111-100000000000000
χ362222-2-2-2-2-2-2-122-1-1-11111-2-22211-1-111-1-100000000-11−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-221-1-1100000000000000
χ372222-2-2-2-2-2-2-122-1-1-11111-2-22211-1-111-1-100000000-11i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-221-1-1100000000000000
χ382222-2-2-2-2-2-2-122-1-1-11111-2-22211-1-111-1-100000000-11i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i32-2-111-100000000000000
χ392-2-22-2-2222-222-22-2-222-2-200002-22-2000000002−22−200000000002−22−22−22−20000000000002i−2i−i2i2−i2i200
χ402-2-22-2-2222-222-22-2-222-2-200002-22-2000000002−22−200000000002−22−22−22−2000000000000−2i2ii2−i2i2−i200
χ412-2-22-2-2222-222-22-2-222-2-200002-22-200000000−22−220000000000−22−22−22−220000000000002i−2ii2−i2i2−i200
χ422-2-22-2-2222-222-22-2-222-2-200002-22-200000000−22−220000000000−22−22−22−22000000000000−2i2i−i2i2−i2i200
χ432-2-22-2-222-222-222-2-222-2-20000-22-22000000002−2−2200000000002−22−2−22−2200000000002i−2i00−i2i2i2−i200
χ442-2-22-2-222-222-222-2-222-2-20000-22-22000000002−2−2200000000002−22−2−22−220000000000−2i2i00i2−i2−i2i200
χ452-2-22-2-222-222-222-2-222-2-20000-22-2200000000−222−20000000000−22−222−22−200000000002i−2i00i2−i2−i2i200
χ462-2-22-2-222-222-222-2-222-2-20000-22-2200000000−222−20000000000−22−222−22−20000000000−2i2i00−i2i2i2−i200
χ474444444444-244-2-2-2-2-2-2-2-4-4-4-4-2-2-2-222220000000022000000000000000000000000000000000000
χ4844444444-4-4-2-4-4-2-2-2-2-2-2-2-44-442222222200000000-2-2000000000000000000000000000000000000
χ494444-4-4-4-444-2-4-4-2-2-222224-4-44-2-222-2-22200000000-22000000000000000000000000000000000000
χ504444-4-4-4-4-4-4-244-2-2-2222244-4-422-2-2-2-222000000002-2000000000000000000000000000000000000
χ5144-4-44i−4i4i−4i00400-44-44i−4i4i−4i000000000000000000000000000000000000000000002-22i−2i0000000000
χ5244-4-44i−4i4i−4i00400-44-44i−4i4i−4i00000000000000000000000000000000000000000000-22−2i2i0000000000
χ5344-4-4−4i4i−4i4i00400-44-4−4i4i−4i4i000000000000000000000000000000000000000000002-2−2i2i0000000000
χ5444-4-4−4i4i−4i4i00400-44-4−4i4i−4i4i00000000000000000000000000000000000000000000-222i−2i0000000000
χ554-44-44i−4i−4i4i00400-4-44−4i4i4i−4i0000000000002i−2i2-20000002i−2i2-22i−2i2-20000000000000000000000000000
χ564-44-44i−4i−4i4i00400-4-44−4i4i4i−4i000000000000−2i2i-22000000−2i2i-22−2i2i-220000000000000000000000000000
χ574-44-44i−4i−4i4i00-20022-22i−2i−2i2i0000000023−23−2i32i32i−2i2-20000002ζ14−2ζ14−1+i31−i32ζ22−2ζ22−1−i31+i30000000000000000000000000000
χ584-44-44i−4i−4i4i00-20022-22i−2i−2i2i0000000023−23−2i32i3−2i2i-22000000−2ζ142ζ141−i3−1+i3−2ζ222ζ221+i3−1−i30000000000000000000000000000
χ594-44-44i−4i−4i4i00-20022-22i−2i−2i2i00000000−23232i3−2i32i−2i2-20000002ζ22−2ζ22−1−i31+i32ζ14−2ζ14−1+i31−i30000000000000000000000000000
χ604-44-44i−4i−4i4i00-20022-22i−2i−2i2i00000000−23232i3−2i3−2i2i-22000000−2ζ222ζ221+i3−1−i3−2ζ142ζ141−i3−1+i30000000000000000000000000000
χ614-44-4−4i4i4i−4i00400-4-444i−4i−4i4i0000000000002i−2i-220000002i−2i-222i−2i-220000000000000000000000000000
χ624-44-4−4i4i4i−4i00400-4-444i−4i−4i4i000000000000−2i2i2-2000000−2i2i2-2−2i2i2-20000000000000000000000000000
χ634-44-4−4i4i4i−4i00-20022-2−2i2i2i−2i0000000023−232i3−2i32i−2i-220000002ζ22−2ζ221+i3−1−i32ζ14−2ζ141−i3−1+i30000000000000000000000000000
χ644-44-4−4i4i4i−4i00-20022-2−2i2i2i−2i0000000023−232i3−2i3−2i2i2-2000000−2ζ222ζ22−1−i31+i3−2ζ142ζ14−1+i31−i30000000000000000000000000000
χ654-44-4−4i4i4i−4i00-20022-2−2i2i2i−2i00000000−2323−2i32i32i−2i-220000002ζ14−2ζ141−i3−1+i32ζ22−2ζ221+i3−1−i30000000000000000000000000000
χ664-44-4−4i4i4i−4i00-20022-2−2i2i2i−2i00000000−2323−2i32i3−2i2i2-2000000−2ζ142ζ14−1+i31−i3−2ζ222ζ22−1−i31+i30000000000000000000000000000
χ674-4-4444-4-44-44-444-4-4-4-44400004-4-4400000000000000000000000000000000000000000000000000
χ684-4-4444-4-44-4-2-44-22222-2-20000-222-20000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000
χ694-4-4444-4-44-4-2-44-22222-2-20000-222-20000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000
χ704-4-4444-4-4-4444-44-4-4-4-4440000-444-400000000000000000000000000000000000000000000000000
χ714-4-4444-4-4-44-24-4-22222-2-200002-2-220000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000
χ724-4-4444-4-4-44-24-4-22222-2-200002-2-220000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000
χ734-4-44-4-4444-4-24-4-222-2-2220000-22-220000000022−2222−220000000000−22−22−22−2200000000000000000000
χ744-4-44-4-4444-4-24-4-222-2-2220000-22-2200000000−2222−222200000000002−22−22−22−200000000000000000000
χ754-4-44-4-444-44-2-44-222-2-22200002-22-20000000022−22−22220000000000−22−222−22−200000000000000000000
χ764-4-44-4-444-44-2-44-222-2-22200002-22-200000000−222222−2200000000002−22−2−22−2200000000000000000000
χ7788-8-88i−8i8i−8i00-4004-44−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ7888-8-8−8i8i−8i8i00-4004-444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000

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