Finite Group Databasebeta

← Group #11886864

Character table — Group #11886864

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222222224444444444444444444444444888888888888888888888121212121818242424242424242424242424242436363636364848484872
order122334466882346666681212121212121212242424242424242466668121212122424242424242424242424242244882244666688121212122444861224248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-11-11-11111-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-1-1-1-1-1-11111-1
χ511111111111-11-111-1-1111-1-11111111111111-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1111-1-111-1
χ611111111111-11-111-1-1111-1-11111111111111-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-11-1111-1-1-1-111-1-111-1-1-111-1-11
χ711111111111-11-111-1-1111-1-11111111111111-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111111-1-1-1
χ811111111111-11-111-1-1111-1-11111111111111-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-11111-1-1-1-1-1111
χ9111111111-1-111111111-111111111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-1-111-1111-11-1-1-111-1-11-111-1-1
χ10111111111-1-111111111-111111111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-11-111-111-1-1-1-1-111-11-1-111
χ11111111111-1-111111111-111111111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-111-1-11-1-1-11-111111-1-111-1-11-1
χ12111111111-1-111111111-111111111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-11-1-11-1-1111-1-111-1-111-11
χ13111111111-1-1-11-111-1-11-11-1-111111-1-1-1-1-1-1-1-1-11-1-11-11-1-1-1-1-1-1111111111-11-111-111-11-1-1-11-11-111-1-1-1-111-11-11
χ14111111111-1-1-11-111-1-11-11-1-111111-1-1-1-1-1-1-1-1-11-1-11-11-1-1-1-1-1-1111111111-11-1-1-1-1-1111-1-1-1-111-1111111-1-11-11-1
χ15111111111-1-1-11-111-1-11-11-1-111111-1-1-1-1-1-1-1-1-11-1-11-11-1-1-1-1-1-111111111-11-11111-1-11-1111-11-11-1-1-1-1-1-11-11-111
χ16111111111-1-1-11-111-1-11-11-1-111111-1-1-1-1-1-1-1-1-11-1-11-11-1-1-1-1-1-111111111-11-11-1-111-1-1-11111-1-11-1-11111-11-11-1-1
χ172222-1222-1222-122-1-1-1-12-1-1-12-1-1-1222-1-1-1-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-12222002020-1-1-1-100-1-1-1-10000000000
χ182222-1222-1222-122-1-1-1-12-1-1-12-1-1-1222-1-1-1-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-200-20-2011110011110000000000
χ192222-1222-122-2-1-22-111-12-1112-1-1-1222-1-1-1-1-1-1-2-111-2-2-1112-1-1-1-2-2111111222200-20-20-1-11100-1-1110000000000
χ202222-1222-122-2-1-22-111-12-1112-1-1-1222-1-1-1-1-1-1-2-111-2-2-1112-1-1-1-2-2111111-2-2-2-200202011-1-10011-1-10000000000
χ212222-1222-1-2-22-122-1-1-1-1-2-1-1-12-1-1-12-2-21111112-1-1-1-22-1-1-1-2111-2-21111112-22-20020-20-11-1-100-11110000000000
χ222222-1222-1-2-22-122-1-1-1-1-2-1-1-12-1-1-12-2-21111112-1-1-1-22-1-1-1-2111-2-2111111-22-2200-20201-111001-1-1-10000000000
χ232222-1222-1-2-2-2-1-22-111-1-2-1112-1-1-12-2-2111111-2-1112-2-111-211122-1-1-1-1-1-12-22-200-2020-111100-11-1-10000000000
χ242222-1222-1-2-2-2-1-22-111-1-2-1112-1-1-12-2-2111111-2-1112-2-111-211122-1-1-1-1-1-1-22-220020-201-1-1-1001-1110000000000
χ25222-1222-12222-12-1222-12222-12-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-122-1-1-1-10000000202000022000000000-1-1-1-10
χ26222-1222-12222-12-1222-12222-12-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-122-1-1-1-10000000-20-20000-2-200000000011110
χ27222-1222-1222-2-1-2-12-2-2-122-2-2-12-1-1-1-1-122-1-1-1-11-111-21-111-12-1-111-2-2111100000002020000-2-2000000000-1-1110
χ28222-1222-1222-2-1-2-12-2-2-122-2-2-12-1-1-1-1-122-1-1-1-11-111-21-111-12-1-111-2-211110000000-20-200002200000000011-1-10
χ29222-1222-12-2-22-12-1222-1-2222-12-1-1-111-2-21111-1-1-1-1-2-1-1-1-11-21111-2-21111000000020-20000-22000000000-111-10
χ30222-1222-12-2-22-12-1222-1-2222-12-1-1-111-2-21111-1-1-1-1-2-1-1-1-11-21111-2-211110000000-20200002-20000000001-1-110
χ31222-1222-12-2-2-2-1-2-12-2-2-1-22-2-2-12-1-1-111-2-211111-11121-1111-211-1-122-1-1-1-1000000020-200002-2000000000-11-110
χ32222-1222-12-2-2-2-1-2-12-2-2-1-22-2-2-12-1-1-111-2-211111-11121-1111-211-1-122-1-1-1-10000000-2020000-220000000001-11-10
χ3322-2222-22222020-2-2002-2-2002222-2222222220-20000-200-2-2-2-2000000002-2-220000002-20000-22000000000000
χ3422-2222-22222020-2-2002-2-2002222-2222222220-20000-200-2-2-2-200000000-222-2000000-2200002-2000000000000
χ3522-2222-222-2-2020-2-20022-2002222-2-2-2-2-2-2-2-2-20-20000-20022220000000022-2-2000000220000-2-2000000000000
χ3622-2222-222-2-2020-2-20022-2002222-2-2-2-2-2-2-2-2-20-20000-200222200000000-2-222000000-2-2000022000000000000
χ3722-222-22220022-2-2-222202-2-2-2-2-2-22000000002-2220-22-2-200000000000000002200000000000000-2200-200000
χ3822-222-22220022-2-2-222202-2-2-2-2-2-22000000002-2220-22-2-20000000000000000-2-2000000000000002-200200000
χ3922-222-222200-222-2-2-2-220222-2-2-2-2200000000-2-2-2-202222000000000000000022000000000000002-200-200000
χ4022-222-222200-222-2-2-2-220222-2-2-2-2200000000-2-2-2-2022220000000000000000-2-200000000000000-2200200000
χ4122-22-12-22-1220-10-21−i3i3-1-21−i3i32-1-1-1-222-1-1-1-1-1-101−i3i3001−i3i3-211100−i3i3−i3−i3i3i32-2-22000000-11−i3i3001-1−i3i30000000000
χ4222-22-12-22-1220-10-21−i3i3-1-21−i3i32-1-1-1-222-1-1-1-1-1-101−i3i3001−i3i3-211100−i3i3−i3−i3i3i3-222-20000001-1i3−i300-11i3−i30000000000
χ4322-22-12-22-1220-10-21i3−i3-1-21i3−i32-1-1-1-222-1-1-1-1-1-101i3−i3001i3−i3-211100i3−i3i3i3−i3−i32-2-22000000-11i3−i3001-1i3−i30000000000
χ4422-22-12-22-1220-10-21i3−i3-1-21i3−i32-1-1-1-222-1-1-1-1-1-101i3−i3001i3−i3-211100i3−i3i3i3−i3−i3-222-20000001-1−i3i300-11−i3i30000000000
χ4522-22-12-22-1-2-20-10-21−i3i3-121−i3i32-1-1-1-2-2-211111101−i3i3001−i3i32-1-1-100i3−i3i3i3−i3−i322-2-2000000-1-1−i3i30011i3−i30000000000
χ4622-22-12-22-1-2-20-10-21−i3i3-121−i3i32-1-1-1-2-2-211111101−i3i3001−i3i32-1-1-100i3−i3i3i3−i3−i3-2-22200000011i3−i300-1-1−i3i30000000000
χ4722-22-12-22-1-2-20-10-21i3−i3-121i3−i32-1-1-1-2-2-211111101i3−i3001i3−i32-1-1-100−i3i3−i3−i3i3i322-2-2000000-1-1i3−i30011−i3i30000000000
χ4822-22-12-22-1-2-20-10-21i3−i3-121i3−i32-1-1-1-2-2-211111101i3−i3001i3−i32-1-1-100−i3i3−i3−i3i3i3-2-22200000011−i3i300-1-1i3−i30000000000
χ4944444-4-44400040440040-400-4-4-4-4-400000000040000-400000000000000000000000000000000000000000000
χ504444-2-4-44-2000-204-2−2i32i3-2022i3−2i3-4222-4000000000-2−2i32i30022i3−2i3000000000000000000000000000000000000000000
χ514444-2-4-44-2000-204-22i3−2i3-202−2i32i3-4222-4000000000-22i3−2i3002−2i32i3000000000000000000000000000000000000000000
χ52444-24-4-4-24000-20-2400-20-4002-4222000000000-20000200000023−230023−2323−23000000000000000000000000000000
χ53444-24-4-4-24000-20-2400-20-4002-4222000000000-200002000000−232300−2323−2323000000000000000000000000000000
χ54444-2-244-2-244414-2-2-2-214-2-2-2-2-211-2-2-2-2-21111-21114-2111-2-211-2-2-2-21111000000000000000000000000000000
χ55444-2-244-2-244-41-4-2-22214-222-2-211-2-2-2-2-2111121-1-1-421-1-1-2-2112222-1-1-1-1000000000000000000000000000000
χ56444-2-244-2-2-4-4414-2-2-2-21-4-2-2-2-2-211-22222-1-1-1-1-2111-4-211122-1-12222-1-1-1-1000000000000000000000000000000
χ57444-2-244-2-2-4-4-41-4-2-2221-4-222-2-211-22222-1-1-1-121-1-1421-1-122-1-1-2-2-2-21111000000000000000000000000000000
χ58444-2-2-4-4-2-200010-2-2−2i32i31022i3−2i322-1-1200003i3i−3i−3i01i3−i300-1−i3i3003i−3i23−2300−33−33000000000000000000000000000000
χ59444-2-2-4-4-2-200010-2-2−2i32i31022i3−2i322-1-120000−3i−3i3i3i01i3−i300-1−i3i300−3i3i−2323003−33−3000000000000000000000000000000
χ60444-2-2-4-4-2-200010-2-22i3−2i3102−2i32i322-1-1200003i3i−3i−3i01−i3i300-1i3−i3003i−3i−2323003−33−3000000000000000000000000000000
χ61444-2-2-4-4-2-200010-2-22i3−2i3102−2i32i322-1-120000−3i−3i3i3i01−i3i300-1i3−i300−3i3i23−2300−33−33000000000000000000000000000000
χ6244-44-2-444-2004-2-4-42-2-2-20-222-422240000000042-2-20-4-222000000000000000000000000000000000000000000
χ6344-44-2-444-200-4-24-4222-20-2-2-2-4222400000000-422204-2-2-2000000000000000000000000000000000000000000
χ6444-4-244-4-24440-202-400-2-4-400-24-2-22-2-244-2-2-2-20200002002-42200000000000000000000000000000000000000
χ6544-4-244-4-24-4-40-202-400-24-400-24-2-2222-4-42222020000200-24-2-200000000000000000000000000000000000000
χ6644-4-24-44-24004-2-42-444-204-4-42-422-200000000-22-2-202-222000000000000000000000000000000000000000000
χ6744-4-24-44-2400-4-242-4-4-4-204442-422-20000000022220-2-2-2-2000000000000000000000000000000000000000000
χ6844-4-2-24-4-2-24401022−2i32i31-42−2i32i3-2-2112-2-2-2-211110-1i3−i300-1i3−i322-1-100−2i32i3i3i3−i3−i3000000000000000000000000000000
χ6944-4-2-24-4-2-244010222i3−2i31-422i3−2i3-2-2112-2-2-2-211110-1−i3i300-1−i3i322-1-1002i3−2i3−i3−i3i3i3000000000000000000000000000000
χ7044-4-2-24-4-2-2-4-401022−2i32i3142−2i32i3-2-21122222-1-1-1-10-1i3−i300-1i3−i3-2-211002i3−2i3−i3−i3i3i3000000000000000000000000000000
χ7144-4-2-24-4-2-2-4-4010222i3−2i31422i3−2i3-2-21122222-1-1-1-10-1−i3i300-1−i3i3-2-21100−2i32i3i3i3−i3−i3000000000000000000000000000000
χ7244-4-2-2-44-2-20041-422-2-210-22222-1-1-200003i3i−3i−3i-2-111021-1-100−3i3i0000−3i3i3i−3i000000000000000000000000000000
χ7344-4-2-2-44-2-20041-422-2-210-22222-1-1-20000−3i−3i3i3i-2-111021-1-1003i−3i00003i−3i−3i3i000000000000000000000000000000
χ7444-4-2-2-44-2-200-414222210-2-2-222-1-1-200003i3i−3i−3i2-1-1-10-211100−3i3i00003i−3i−3i3i000000000000000000000000000000
χ7544-4-2-2-44-2-200-414222210-2-2-222-1-1-20000−3i−3i3i3i2-1-1-10-2111003i−3i0000−3i3i3i−3i000000000000000000000000000000
χ764-404400-4-4−2i22i20400000-4000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000−2i22i200000000000000002-2000000
χ774-404400-4-4−2i22i20400000-4000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000002i2−2i20000000000000000-22000000
χ784-404400-4-42i2−2i20400000-40000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000−2i22i20000000000000000-22000000
χ794-404400-4-42i2−2i20400000-40000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000002i2−2i200000000000000002-2000000
χ808-808-400-84−4i24i20-4000004000000000−4i24i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000000
χ818-808-400-844i2−4i20-40000040000000004i2−4i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000000000000000000
χ828-80-48004-8−4i24i20-40000040000000002i2−2i2−4i24i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000000
χ838-80-48004-84i2−4i20-4000004000000000−2i22i24i2−4i2−2i22i2−2i22i2000000000000000000000000000000000000000000000000000
χ848-80-4-40044−4i24i20200000-20000006i−6i02i2−2i22i2−2i2−4ζ5+2ζ7−4ζ13+2ζ234ζ5−2ζ7+4ζ13−2ζ232ζ5−4ζ7+2ζ13−4ζ23−2ζ5+4ζ7−2ζ13+4ζ23000000000000000000000000000000000000000000000000000
χ858-80-4-40044−4i24i20200000-2000000−6i6i02i2−2i22i2−2i22ζ5−4ζ7+2ζ13−4ζ23−2ζ5+4ζ7−2ζ13+4ζ23−4ζ5+2ζ7−4ζ13+2ζ234ζ5−2ζ7+4ζ13−2ζ23000000000000000000000000000000000000000000000000000
χ868-80-4-400444i2−4i20200000-20000006i−6i0−2i22i2−2i22i24ζ5−2ζ7+4ζ13−2ζ23−4ζ5+2ζ7−4ζ13+2ζ23−2ζ5+4ζ7−2ζ13+4ζ232ζ5−4ζ7+2ζ13−4ζ23000000000000000000000000000000000000000000000000000
χ878-80-4-400444i2−4i20200000-2000000−6i6i0−2i22i2−2i22i2−2ζ5+4ζ7−2ζ13+4ζ232ζ5−4ζ7+2ζ13−4ζ234ζ5−2ζ7+4ζ13−2ζ23−4ζ5+2ζ7−4ζ13+2ζ23000000000000000000000000000000000000000000000000000

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