Finite Group Databasebeta

← Group #11791048

Character table — Group #11791048

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222444444444444444444446666666666666666888888999912121212121212121212121212121212181818181818242424244848484872727272
order1222448888336666661212121224242424242424244444444488888888121224242424222212121212121212122424242424242424448888222266664444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ5111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1
χ6111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111
χ7111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-111
χ8111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-11111-1-1
χ91-1-11-1111-1-111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-11-11-11-11-1i−ii−i
χ101-1-11-1111-1-111-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1-11-11-11-11−ii−ii
χ111-1-11-1111-1-111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-11-11-11-11-1−ii−ii
χ121-1-11-1111-1-111-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1-11-11-11-11i−ii−i
χ131-1-11-11-1-11111-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1-1111-1-111-1-11i−i−ii
χ141-1-11-11-1-11111-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-1-111-111-1-111-1−iii−i
χ151-1-11-11-1-11111-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1111-1-111-1-11−iii−i
χ161-1-11-11-1-11111-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111-111-1-111-1i−i−ii
χ172222222222222222222222222222220000000000000000222222-2-2-2-20000000000000000-2-2-2-2-2-2000000000000
χ18222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2000000000000000022-2-2-2-2-2-2-2-20000000000000000-2-22222000000000000
χ192222-2-2000022222222-2-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i-2-20000-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i220000000000000000
χ202222-2-2000022222222-2-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i-2-20000-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i220000000000000000
χ212222-2-2000022222222-2-2-2-20000000022-2-222-2-200000000-2-20000222222-2-222-2-200000000-2-20000000000000000
χ222222-2-2000022222222-2-2-2-200000000-2-222-2-22200000000-2-200002222-2-222-2-22200000000-2-20000000000000000
χ2322-2-2002−22−2222-2-2-22-2000022−2−222−2−2002i−2i002i−2ii2−i2i2−i2i2−i2i2−i2002−22−22-22-2002i−2i002i−2ii2−i2i2−i2i2−i2i2−i2002−22−2000000000000
χ2422-2-2002−22−2222-2-2-22-2000022−2−222−2−200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i2002−22−22-22-200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i2002−22−2000000000000
χ2522-2-2002−22−2222-2-2-22-2000022−2−222−2−22-2002-2002−2−222−2−22002−22−2-22-222-2002-2002−2−222−2−2200−22−22000000000000
χ2622-2-2002−22−2222-2-2-22-2000022−2−222−2−2-2200-2200−222−2−222−2002−22−2-22-22-2200-2200−222−2−222−200−22−22000000000000
χ2722-2-200−22−22222-2-2-22-20000−2−222−2−222002i−2i002i−2i−i2i2−i2i2−i2i2−i2i200−22−222-22-2002i−2i002i−2i−i2i2−i2i2−i2i2−i2i200−22−22000000000000
χ2822-2-200−22−22222-2-2-22-20000−2−222−2−22200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i200−22−222-22-200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i200−22−22000000000000
χ2922-2-200−22−22222-2-2-22-20000−2−222−2−2222-2002-200−222−2−222−200−22−22-22-222-2002-200−222−2−222−2002−22−2000000000000
χ3022-2-200−22−22222-2-2-22-20000−2−222−2−222-2200-22002−2−222−2−2200−22−22-22-22-2200-22002−2−222−2−22002−22−2000000000000
χ312-22-2002−2−2222-22-2-2-22000022−2−2−2−222002-200-222−22−2−22−22002−2−222-2-22002-200-222−22−2−22−22002−2−22000000000000
χ322-22-2002−2−2222-22-2-2-22000022−2−2−2−22200-22002-2−22−222−22−2002−2−222-2-2200-22002-2−22−222−22−2002−2−22000000000000
χ332-22-2002−2−2222-22-2-2-22000022−2−2−2−2222i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i2002−2−22-222-22i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i200−222−2000000000000
χ342-22-2002−2−2222-22-2-2-22000022−2−2−2−222−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i2002−2−22-222-2−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i200−222−2000000000000
χ352-22-200−222−222-22-2-2-220000−2−22222−2−2002-200-22−22−222−22−200−222−22-2-22002-200-22−22−222−22−200−222−2000000000000
χ362-22-200−222−222-22-2-2-220000−2−22222−2−200-22002-22−22−2−22−2200−222−22-2-2200-22002-22−22−2−22−2200−222−2000000000000
χ372-22-200−222−222-22-2-2-220000−2−22222−2−22i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i200−222−2-222-22i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i2002−2−22000000000000
χ382-22-200−222−222-22-2-2-220000−2−22222−2−2−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i200−222−2-222-2−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i2002−2−22000000000000
χ392-2-222-2000022-2-222-2-2-2-222000000000000000022-2-2-2-2222-20000-2-2220000000022-2-2-2-2222-20000000000000000
χ402-2-222-2000022-2-222-2-2-2-2220000000000000000-2-22222-2-22-20000-2-22200000000-2-22222-2-22-20000000000000000
χ412-2-222-2000022-2-222-2-2-2-222000000002i2i−2i−2i−2i−2i2i2i000000002-2000022-2-22i2i−2i−2i−2i−2i2i2i00000000-220000000000000000
χ422-2-222-2000022-2-222-2-2-2-22200000000−2i−2i2i2i2i2i−2i−2i000000002-2000022-2-2−2i−2i2i2i2i2i−2i−2i00000000-220000000000000000
χ432-2-22-2222-2-222-2-222-2-222-2-22222-2-2-2-20000000000000000-2222-2-2-2-2220000000000000000-22-2-222000000000000
χ442-2-22-22-2-22222-2-222-2-222-2-2-2-2-2-222220000000000000000-22-2-222-2-2220000000000000000-2222-2-2000000000000
χ4544444444441-2-2-21-2111111111111112222222222222222-2-2-2-2-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ4644444444441-2-2-21-211111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200001111111111111111000000000000000000
χ474444444444-2111-21-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000111111000000000000000000000000002222-1-1-1-10000
χ484444444444-2111-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000011111100000000000000000000000000-2-2-2-211110000
χ49444444-4-4-4-41-2-2-21-2111111-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-2-222220000-1-1-1-1-1-1-1-111111111000000000000000000
χ50444444-4-4-4-41-2-2-21-2111111-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222222222-2-22222000011111111-1-1-1-1-1-1-1-1000000000000000000
χ51444444-4-4-4-4-2111-21-2-2-2-2-2-222222222000000000000000011-1-1-1-10000000000000000000000000022-2-2-1-1110000
χ52444444-4-4-4-4-2111-21-2-2-2-2-2-222222222000000000000000011-1-1-1-100000000000000000000000000-2-22211-1-10000
χ534444-4-400001-2-2-21-211-1-1-1-13i−3i3i−3i3i−3i3i−3i22-2-222-2-22i2i−2i−2i2i2i−2i−2i2200000000-1-111-1-111−i−iii−i−iii000000000000000000
χ544444-4-400001-2-2-21-211-1-1-1-13i−3i3i−3i3i−3i3i−3i-2-222-2-222−2i−2i2i2i−2i−2i2i2i220000000011-1-111-1-1ii−i−iii−i−i000000000000000000
χ554444-4-400001-2-2-21-211-1-1-1-1−3i3i−3i3i−3i3i−3i3i22-2-222-2-2−2i−2i2i2i−2i−2i2i2i2200000000-1-111-1-111ii−i−iii−i−i000000000000000000
χ564444-4-400001-2-2-21-211-1-1-1-1−3i3i−3i3i−3i3i−3i3i-2-222-2-2222i2i−2i−2i2i2i−2i−2i220000000011-1-111-1-1−i−iii−i−iii000000000000000000
χ5744-4-40022−2222−221-2-22-121-13i−3i3i−3i2ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32-22i−2i2-22i−2i2ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300−22−220000-11−ii-11−ii−ζζ−ζ3ζ3−ζζ−ζ3ζ3000000000000000000
χ5844-4-40022−2222−221-2-22-121-13i−3i3i−3i2ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3-22−2i2i-22−2i2i−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300−22−2200001-1i−i1-1i−iζ−ζζ3−ζ3ζ−ζζ3−ζ3000000000000000000
χ5944-4-40022−2222−221-2-22-121-1−3i3i−3i3i−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ32-2−2i2i2-2−2i2i−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00−22−220000-11i−i-11i−iζ3−ζ3ζ−ζζ3−ζ3ζ−ζ000000000000000000
χ6044-4-40022−2222−221-2-22-121-1−3i3i−3i3i−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3-222i−2i-222i−2i2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00−22−2200001-1−ii1-1−ii−ζ3ζ3−ζζ−ζ3ζ3−ζζ000000000000000000
χ6144-4-400−2222−22221-2-22-121-13i−3i3i−3i−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32-22i−2i2-22i−2i−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3002−22−20000-11−ii-11−iiζ−ζζ3−ζ3ζ−ζζ3−ζ3000000000000000000
χ6244-4-400−2222−22221-2-22-121-13i−3i3i−3i−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3-22−2i2i-22−2i2i2ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3002−22−200001-1i−i1-1i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3000000000000000000
χ6344-4-400−2222−22221-2-22-121-1−3i3i−3i3iζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ32-2−2i2i2-2−2i2i2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ002−22−20000-11i−i-11i−i−ζ3ζ3−ζζ−ζ3ζ3−ζζ000000000000000000
χ6444-4-400−2222−22221-2-22-121-1−3i3i−3i3iζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3-222i−2i-222i−2i−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ002−22−200001-1−ii1-1−iiζ3−ζ3ζ−ζζ3−ζ3ζ−ζ000000000000000000
χ654-44-40022−22−22221-22-2-12-113i−3i−3i3i2ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32i−2i-22−2i2i2-22ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ00−222−20000−ii1-1i−i-11−ζ3ζ3ζ−ζζ3−ζ3−ζζ000000000000000000
χ664-44-40022−22−22221-22-2-12-113i−3i−3i3i2ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2i2i2-22i−2i-22−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ00−222−20000i−i-11−ii1-1ζ3−ζ3−ζζ−ζ3ζ3ζ−ζ000000000000000000
χ674-44-40022−22−22221-22-2-12-11−3i3i3i−3i−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ32i−2i2-2−2i2i-222ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ300−222−20000−ii-11i−i1-1−ζζζ3−ζ3ζ−ζ−ζ3ζ3000000000000000000
χ684-44-40022−22−22221-22-2-12-11−3i3i3i−3i−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−2i2i-222i−2i2-2−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ300−222−20000i−i1-1−ii-11ζ−ζ−ζ3ζ3−ζζζ3−ζ3000000000000000000
χ694-44-400−222222−221-22-2-12-113i−3i−3i3i−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32i−2i-22−2i2i2-2−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ002−2−220000−ii1-1i−i-11ζ3−ζ3−ζζ−ζ3ζ3ζ−ζ000000000000000000
χ704-44-400−222222−221-22-2-12-113i−3i−3i3i−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−2i2i2-22i−2i-222ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ002−2−220000i−i-11−ii1-1−ζ3ζ3ζ−ζζ3−ζ3−ζζ000000000000000000
χ714-44-400−222222−221-22-2-12-11−3i3i3i−3iζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ32i−2i2-2−2i2i-22−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3002−2−220000−ii-11i−i1-1ζ−ζ−ζ3ζ3−ζζζ3−ζ3000000000000000000
χ724-44-400−222222−221-22-2-12-11−3i3i3i−3iζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−2i2i-222i−2i2-22ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3002−2−220000i−i1-1−ii-11−ζζζ3−ζ3ζ−ζ−ζ3ζ3000000000000000000
χ734-4-444-400001-2221-2-1-1-1-1113i−3i3i−3i−3i3i−3i3i2i2i−2i−2i−2i−2i2i2i-2-22222-2-2-2200000000−i−iiiii−i−i11-1-1-1-111000000000000000000
χ744-4-444-400001-2221-2-1-1-1-1113i−3i3i−3i−3i3i−3i3i−2i−2i2i2i2i2i−2i−2i22-2-2-2-222-2200000000ii−i−i−i−iii-1-11111-1-1000000000000000000
χ754-4-444-400001-2221-2-1-1-1-111−3i3i−3i3i3i−3i3i−3i2i2i−2i−2i−2i−2i2i2i22-2-2-2-222-2200000000−i−iiiii−i−i-1-11111-1-1000000000000000000
χ764-4-444-400001-2221-2-1-1-1-111−3i3i−3i3i3i−3i3i−3i−2i−2i2i2i2i2i−2i−2i-2-22222-2-2-2200000000ii−i−i−i−iii11-1-1-1-111000000000000000000
χ774-4-44-4444-4-41-2221-2-1-111-1-11111-1-1-1-12i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2-2-2-2220000−i−i−i−iiiii−i−i−i−iiiii000000000000000000
χ784-4-44-4444-4-41-2221-2-1-111-1-11111-1-1-1-1−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i2-2-2-2220000iiii−i−i−i−iiiii−i−i−i−i000000000000000000
χ794-4-44-4444-4-4-21-1-1-2122-2-222-2-2-2-222220000000000000000-1111-1-1000000000000000000000000002-22-2-11-110000
χ804-4-44-4444-4-4-21-1-1-2122-2-222-2-2-2-222220000000000000000-1111-1-100000000000000000000000000-22-221-11-10000
χ814-4-44-44-4-4441-2221-2-1-111-1-1-1-1-1-111112i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2-222-2-20000−i−i−i−iiiiiiiii−i−i−i−i000000000000000000
χ824-4-44-44-4-4441-2221-2-1-111-1-1-1-1-1-11111−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i2-222-2-20000iiii−i−i−i−i−i−i−i−iiiii000000000000000000
χ834-4-44-44-4-444-21-1-1-2122-2-2222222-2-2-2-20000000000000000-11-1-111000000000000000000000000002-2-22-111-10000
χ844-4-44-44-4-444-21-1-1-2122-2-2222222-2-2-2-20000000000000000-11-1-11100000000000000000000000000-222-21-1-110000
χ858888-8-80000-4222-42-4-44444000000000000000000000000-2-2000000000000000000000000000000000000000000
χ8688-8-80042−4242−42-422-24-2-440000−22−222222−22−2222220000000000000000002−22−200000000000000000000000000000000000000
χ8788-8-800−4242−4242-422-24-2-4400002222−22−222222−22−22000000000000000000−22−2200000000000000000000000000000000000000
χ888-88-80042−42−4242-42-224-24-40000−22−2222222222−22−220000000000000000002−2−2200000000000000000000000000000000000000
χ898-88-800−424242−42-42-224-24-400002222−22−22−22−222222000000000000000000−222−200000000000000000000000000000000000000
χ908-8-888-80000-42-2-2-424444-4-40000000000000000000000002-2000000000000000000000000000000000000000000

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