Finite Group Databasebeta

← Group #11785296

Character table — Group #11785296

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222444444444444444448888888899991212121212121212121212121212121218181818242424242424242424242424242424243672727272
order12224444334666666121212121212121212121212121212122222444444448888888844441212121212121212242424242424242444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1111111-1-1-1-1iiii−i−i−i−i1ii−i−i
χ6111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1111111-1-1-1-1−i−i−i−iiiii1−i−iii
χ7111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-111-1-1-1-11111iiii−i−i−i−i1−i−iii
χ8111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-111-1-1-1-11111−i−i−i−iiiii1ii−i−i
χ91111-1-11111-1111111-1-1-1-11111-1-1-1-111-1-1111111-1-111-1-111-1-111-1-1-1-11111-1-111-1-111-1-111-1-1-11-11-1
χ101111-1-11111-1111111-1-1-1-11111-1-1-1-111-1-1111111-1-111-1-1-1-111-1-111-1-11111-1-111-1-1-1-111-1-111-1-11-11
χ111111-1-11111-1111111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-11111-1-111-1-1-1-111-1-111-1-11111-1-111-1-1-1-11-11
χ121111-1-11111-1111111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-11-11-1
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-111ii−i−i−i−iii111111-1-1-1-111ii−i−i−i−iii-1i−i−ii
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-111−i−iiiii−i−i111111-1-1-1-111−i−iiiii−i−i-1−iii−i
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1ii−i−i−i−iii1111-1-11111-1-1ii−i−i−i−iii-1−iii−i
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1−i−iiiii−i−i1111-1-11111-1-1−i−iiiii−i−i-1i−i−ii
χ17222222222222222222222222222222222-2-2-2-20000000000000000-2-2-2-20000000000000000-20000
χ18222222-2-222-22222222222-2-2-2-222-2-2-2-2-2-22222000000000000000022-2-20000000000000000-20000
χ192222-2-22222-2222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-2000000000000000022-2-2000000000000000020000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-222-2-22222220000000000000000-2-2-2-2000000000000000020000
χ212-22-2002-22202-2-2-22-2000022-2-200002-20022-2-2002-2002-200000000002-2002-2002-20000000000000
χ222-22-2002-22202-2-2-22-2000022-2-200002-20022-2-200-2200-2200000000002-200-2200-220000000000000
χ232-22-2002-22202-2-2-22-2000022-2-200002-200-2-2222i−2i002i−2i000000000000-222i−2i002i−2i000000000000000
χ242-22-2002-22202-2-2-22-2000022-2-200002-200-2-222−2i2i00−2i2i000000000000-22−2i2i00−2i2i000000000000000
χ252-22-200-222202-2-2-22-20000-2-2220000-220022-2-22i−2i00−2i2i000000000000-222i−2i00−2i2i000000000000000
χ262-22-200-222202-2-2-22-20000-2-2220000-220022-2-2−2i2i002i−2i000000000000-22−2i2i002i−2i000000000000000
χ272-22-200-222202-2-2-22-20000-2-2220000-2200-2-222002-200-2200000000002-2002-200-220000000000000
χ282-22-200-222202-2-2-22-20000-2-2220000-2200-2-22200-22002-200000000002-200-22002-20000000000000
χ292-2-222i−2i00220-22-2-2-222i2i−2i−2i00002i−2i0000002-22-200000000i2−i22−2i2−i22−22i−2i0000000000i2−i22−2i2−i22−200000
χ302-2-222i−2i00220-22-2-2-222i2i−2i−2i00002i−2i0000002-22-200000000−i2i2−22−i2i2−222i−2i0000000000−i2i2−22−i2i2−2200000
χ312-2-222i−2i00220-22-2-2-222i2i−2i−2i00002i−2i000000-22-22000000002−2−i2i2−22i2−i2−2i2i00000000002−2−i2i2−22i2−i200000
χ322-2-222i−2i00220-22-2-2-222i2i−2i−2i00002i−2i000000-22-2200000000−22i2−i22−2−i2i2−2i2i0000000000−22i2−i22−2−i2i200000
χ332-2-22−2i2i00220-22-2-2-22−2i−2i2i2i0000−2i2i0000002-22-200000000i2−i2−22i2−i2−22−2i2i0000000000i2−i2−22i2−i2−2200000
χ342-2-22−2i2i00220-22-2-2-22−2i−2i2i2i0000−2i2i0000002-22-200000000−i2i22−2−i2i22−2−2i2i0000000000−i2i22−2−i2i22−200000
χ352-2-22−2i2i00220-22-2-2-22−2i−2i2i2i0000−2i2i000000-22-22000000002−2i2−i2−22−i2i22i−2i00000000002−2i2−i2−22−i2i200000
χ362-2-22−2i2i00220-22-2-2-22−2i−2i2i2i0000−2i2i000000-22-2200000000−22−i2i22−2i2−i22i−2i0000000000−22−i2i22−2i2−i200000
χ37444444441-24111-2-2-2-2-2-2-211111111-2-2-2-200000000000022222222000000000000-1-1-1-1-1-1-1-100000
χ38444444441-24111-2-2-2-2-2-2-211111111-2-2-2-2000000000000-2-2-2-2-2-2-2-20000000000001111111100000
χ3944444444-214-2-2-21111111-2-2-2-2-2-2-2-21111000022222222000000000000-1-1-1-1-1-1-1-10000000000000
χ4044444444-214-2-2-21111111-2-2-2-2-2-2-2-211110000-2-2-2-2-2-2-2-2000000000000111111110000000000000
χ41444444-4-41-2-4111-2-2-2-2-2-2-2-1-1-1-111-1-122220000000000002i2i2i2i−2i−2i−2i−2i000000000000−i−i−i−iiiii00000
χ42444444-4-41-2-4111-2-2-2-2-2-2-2-1-1-1-111-1-12222000000000000−2i−2i−2i−2i2i2i2i2i000000000000iiii−i−i−i−i00000
χ43444444-4-4-21-4-2-2-211111112222-2-222-1-1-1-100002222-2-2-2-2000000000000-1-1-1-111110000000000000
χ44444444-4-4-21-4-2-2-211111112222-2-222-1-1-1-10000-2-2-2-222220000000000001111-1-1-1-10000000000000
χ454444-4-4441-2-4111-2-2-222221111-1-1-1-1-2-22200000000000022-2-222-2-2000000000000-1-111-1-11100000
χ464444-4-4441-2-4111-2-2-222221111-1-1-1-1-2-222000000000000-2-222-2-22200000000000011-1-111-1-100000
χ474444-4-444-21-4-2-2-2111-1-1-1-1-2-2-2-2222211-1-1000022-2-222-2-2000000000000-1-111-1-1110000000000000
χ484444-4-444-21-4-2-2-2111-1-1-1-1-2-2-2-2222211-1-10000-2-222-2-22200000000000011-1-111-1-10000000000000
χ494444-4-4-4-41-24111-2-2-22222-1-1-1-1-1-11122-2-20000000000002i2i−2i−2i−2i−2i2i2i000000000000−i−iiiii−i−i00000
χ504444-4-4-4-41-24111-2-2-22222-1-1-1-1-1-11122-2-2000000000000−2i−2i2i2i2i2i−2i−2i000000000000ii−i−i−i−iii00000
χ514444-4-4-4-4-214-2-2-2111-1-1-1-1222222-2-2-1-111000022-2-2-2-222000000000000-1-11111-1-10000000000000
χ524444-4-4-4-4-214-2-2-2111-1-1-1-1222222-2-2-1-1110000-2-22222-2-200000000000011-1-1-1-1110000000000000
χ5344-4-40000440-4-444-4-400000000000000004-4-4400000000000000000000000000000000000000000
χ5444-4-40000440-4-444-4-40000000000000000-444-400000000000000000000000000000000000000000
χ554-44-4004-4-210-222-11-13i−3i3i−3i-2-22200001-13i−3i00002i−2i2-22i−2i2-2000000000000−ii-11−ii-110000000000000
χ564-44-4004-4-210-222-11-13i−3i3i−3i-2-22200001-13i−3i0000−2i2i-22−2i2i-22000000000000i−i1-1i−i1-10000000000000
χ574-44-4004-4-210-222-11-1−3i3i−3i3i-2-22200001-1−3i3i00002i−2i-222i−2i-22000000000000−ii1-1−ii1-10000000000000
χ584-44-4004-4-210-222-11-1−3i3i−3i3i-2-22200001-1−3i3i0000−2i2i2-2−2i2i2-2000000000000i−i-11i−i-110000000000000
χ594-44-400-44-210-222-11-13i−3i3i−3i22-2-20000-11−3i3i00002i−2i2-2−2i2i-22000000000000−ii-11i−i1-10000000000000
χ604-44-400-44-210-222-11-13i−3i3i−3i22-2-20000-11−3i3i0000−2i2i-222i−2i2-2000000000000i−i1-1−ii-110000000000000
χ614-44-400-44-210-222-11-1−3i3i−3i3i22-2-20000-113i−3i00002i−2i-22−2i2i2-2000000000000−ii1-1i−i-110000000000000
χ624-44-400-44-210-222-11-1−3i3i−3i3i22-2-20000-113i−3i0000−2i2i2-22i−2i-22000000000000i−i-11−ii1-10000000000000
χ634-4-444i−4i001-20-11-122-2−2i−2i2i2i3i−3i3i−3ii−i3-300000000000000002ζ−2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ000000000000−ζζζ3−ζ3−ζ3ζ3−ζζ00000
χ644-4-444i−4i001-20-11-122-2−2i−2i2i2i3i−3i3i−3ii−i3-30000000000000000−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ000000000000ζ−ζ−ζ3ζ3ζ3−ζ3ζ−ζ00000
χ654-4-444i−4i001-20-11-122-2−2i−2i2i2i−3i3i−3i3ii−i-3300000000000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ3000000000000−ζ3ζ3−ζζ−ζζζ3−ζ300000
χ664-4-444i−4i001-20-11-122-2−2i−2i2i2i−3i3i−3i3ii−i-330000000000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ3000000000000ζ3−ζ3ζ−ζζ−ζ−ζ3ζ300000
χ674-4-44−4i4i001-20-11-122-22i2i−2i−2i3i−3i3i−3i−ii-3300000000000000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ2ζ000000000000−ζζ−ζ3ζ3−ζ3ζ3ζ−ζ00000
χ684-4-44−4i4i001-20-11-122-22i2i−2i−2i3i−3i3i−3i−ii-330000000000000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ−2ζ000000000000ζ−ζζ3−ζ3ζ3−ζ3−ζζ00000
χ694-4-44−4i4i001-20-11-122-22i2i−2i−2i−3i3i−3i3i−ii3-300000000000000002ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3000000000000−ζ3ζ3ζ−ζ−ζζ−ζ3ζ300000
χ704-4-44−4i4i001-20-11-122-22i2i−2i−2i−3i3i−3i3i−ii3-30000000000000000−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ3000000000000ζ3−ζ3−ζζζ−ζζ3−ζ300000
χ7188-8-800002-40-2-22-44400006i−6i−6i6i00000000000000000000000000000000000000000000000000000
χ7288-8-800002-40-2-22-4440000−6i6i6i−6i00000000000000000000000000000000000000000000000000000
χ7388-8-80000-42044-42-2-26-6-66000000000000000000000000000000000000000000000000000000000
χ7488-8-80000-42044-42-2-2-666-6000000000000000000000000000000000000000000000000000000000
χ758-88-8008-82-402-2-24-44000022-2-20000-4400000000000000000000000000000000000000000000000
χ768-88-800-882-402-2-24-440000-2-22200004-400000000000000000000000000000000000000000000000
χ778-8-888i−8i00-4204-44-2-222i2i−2i−2i0000−4i4i000000000000000000000000000000000000000000000000000
χ788-8-88−8i8i00-4204-44-2-22−2i−2i2i2i00004i−4i000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.