Finite Group Databasebeta

← Group #72343791

Character table — Group #72343791

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size11112222226666666612121212121212121212121212121212161616163232323232323232484848484848484848484848484848484848484848484848484848484848484848484848646464646464646464646464
order12222244442222444422222222444444442222366666664444444444444444444444444444888888886666666612121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ31111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ51111-1-11-1-11-1-1111-1-1111-1-1-1-1111111-1-1-1-111-1-1111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1
χ61111-1-11-1-11-1-1111-1-1111-1-1-1-1111111-1-1-1-111-1-1111-1-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-111-1-1
χ71111-1-11-1-11-1-1111-1-1111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1111111-1-1
χ81111-1-11-1-11-1-1111-1-1111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-11-1-111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1
χ91-1-111-111-1-11-11-111-1-11111-1-1-1-111-1-111-1-11-11-11-1-111-1-11i−ii−i1-11-1i−ii−iii−i−iii−i−iii−i−iii−i−ii−ii−ii−ii−i11-1-111-1-11-11-1
χ101-1-111-111-1-11-11-111-1-11111-1-1-1-111-1-111-1-11-11-11-1-111-1-11−ii−ii1-11-1−ii−ii−i−iii−i−iii−i−iii−i−iii−ii−ii−ii−ii11-1-111-1-11-11-1
χ111-1-111-111-1-11-11-111-1-11111-1-1-1-111-1-111-1-1-11-111-1-111-1-11i−ii−i-11-11i−ii−iii−i−iii−i−i−i−iii−i−iii−ii−ii−ii−ii-1-111-1-1111-11-1
χ121-1-111-111-1-11-11-111-1-11111-1-1-1-111-1-111-1-1-11-111-1-111-1-11−ii−ii-11-11−ii−ii−i−iii−i−iiiii−i−iii−i−ii−ii−ii−ii−i-1-111-1-1111-11-1
χ131-1-11-111-11-1-111-11-11-111-1-111-1-111-1-1-1-1111-1-111-1-1-1-1111i−i−ii1-1-11i−i−iiii−i−i−i−iiiii−i−i−i−iiii−i−iii−i−ii11-1-1-1-1111-1-11
χ141-1-11-111-11-1-111-11-11-111-1-111-1-111-1-1-1-1111-1-111-1-1-1-1111−iii−i1-1-11−iii−i−i−iiiii−i−i−i−iiiii−i−i−iii−i−iii−i11-1-1-1-1111-1-11
χ151-1-11-111-11-1-111-11-11-111-1-111-1-111-1-1-1-111-111-11-1-1-1-1111i−i−ii-111-1i−i−iiii−i−i−i−iii−i−iiiii−i−i−iii−i−iii−i-1-11111-1-11-1-11
χ161-1-11-111-11-1-111-11-11-111-1-111-1-111-1-1-1-111-111-11-1-1-1-1111−iii−i-111-1−iii−i−i−iiiii−i−iii−i−i−i−iiii−i−iii−i−ii-1-11111-1-11-1-11
χ1722222222222222222222222222222222222222-1-1-1-1-1-1-1-1000022220000000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1
χ182222222222222222222222222222222222-2-2-2-2-1-1-1-1-1-1-1-10000-2-2-2-2000000000000000000000000000011111111-1-1-1-1
χ19222222-2-2-2-22222-2-2-2-22-22-22-22-22-22-22-22-200002222222200000000000000000000000000000000000000000000-2-2-2-2
χ20222222-2-2-2-22222-2-2-2-22-22-22-22-22-22-22-22-20000-1-1-1-1-1-1-1-1000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i31111
χ21222222-2-2-2-22222-2-2-2-22-22-22-22-22-22-22-22-20000-1-1-1-1-1-1-1-1000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i31111
χ222222-2-22-2-22-2-2222-2-2222-2-2-2-2222222-2-2-2-222-2-2-1-1-11111-1000022-2-20000000000000000000000000000-1-1-1-11111-1-111
χ232222-2-22-2-22-2-2222-2-2222-2-2-2-2222222-2-2-2-2-2-222-1-1-11111-10000-2-22200000000000000000000000000001111-1-1-1-1-1-111
χ242222-2-2-222-2-2-222-222-22-2-22-222-22-22-2-22-220000222-2-2-2-2200000000000000000000000000000000000000000000-2-222
χ252222-2-2-222-2-2-222-222-22-2-22-222-22-22-2-22-220000-1-1-11111-1000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i311-1-1
χ262222-2-2-222-2-2-222-222-22-2-22-222-22-22-2-22-220000-1-1-11111-1000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i311-1-1
χ272-2-222-222-2-22-22-222-2-22222-2-2-2-222-2-222-2-22-22-2-111-1-111-100002-22-20000000000000000000000000000-1-111-1-111-11-11
χ282-2-222-222-2-22-22-222-2-22222-2-2-2-222-2-222-2-2-22-22-111-1-111-10000-22-22000000000000000000000000000011-1-111-1-1-11-11
χ292-2-222-2-2-2222-22-2-2-2222-22-2-22-222-2-222-2-2200002-2-222-2-2200000000000000000000000000000000000000000000-22-22
χ302-2-222-2-2-2222-22-2-2-2222-22-2-22-222-2-222-2-220000-111-1-111-1000000000000000000000000000000000000−i3i3i3−i3−i3i3i3−i31-11-1
χ312-2-222-2-2-2222-22-2-2-2222-22-2-22-222-2-222-2-220000-111-1-111-1000000000000000000000000000000000000i3−i3−i3i3i3−i3−i3i31-11-1
χ322-2-22-222-22-2-222-22-22-222-2-222-2-222-2-2-2-2222-2-22-11111-1-1-100002-2-220000000000000000000000000000-1-11111-1-1-111-1
χ332-2-22-222-22-2-222-22-22-222-2-222-2-222-2-2-2-222-222-2-11111-1-1-10000-222-2000000000000000000000000000011-1-1-1-111-111-1
χ342-2-22-22-22-22-222-2-22-222-2-222-2-222-2-22-222-200002-2-2-2-222200000000000000000000000000000000000000000000-222-2
χ352-2-22-22-22-22-222-2-22-222-2-222-2-222-2-22-222-20000-11111-1-1-1000000000000000000000000000000000000−i3i3i3−i3i3−i3−i3i31-1-11
χ362-2-22-22-22-22-222-2-22-222-2-222-2-222-2-22-222-20000-11111-1-1-1000000000000000000000000000000000000i3−i3−i3i3−i3i3i3−i31-1-11
χ37333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333000000001111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000
χ38333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333300000000-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000
χ39333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-300000000111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ40333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-300000000-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000
χ413333-3-33-3-33-3-3333-3-33-1-11111-1-1-1-1-1-1111133-3-30000000011-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1000000000000
χ423333-3-33-3-33-3-3333-3-33-1-11111-1-1-1-1-1-1111133-3-300000000-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111000000000000
χ433333-3-33-3-33-3-3333-3-33-1-11111-1-1-1-1-1-11111-3-3330000000011-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111000000000000
χ443333-3-33-3-33-3-3333-3-33-1-11111-1-1-1-1-1-11111-3-33300000000-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1000000000000
χ453-3-333-333-3-33-33-333-3-3-1-1-1-11111-1-111-1-1113-33-300000000i−ii−i-11-11i−ii−i−i−iii−i−iii−i−iii−i−iiii−ii−ii−ii−i000000000000
χ463-3-333-333-3-33-33-333-3-3-1-1-1-11111-1-111-1-1113-33-300000000−ii−ii-11-11−ii−iiii−i−iii−i−iii−i−iii−i−i−ii−ii−ii−ii000000000000
χ473-3-333-333-3-33-33-333-3-3-1-1-1-11111-1-111-1-111-33-3300000000i−ii−i1-11-1i−ii−i−i−iii−i−iiiii−i−iii−i−i−ii−ii−ii−ii000000000000
χ483-3-333-333-3-33-33-333-3-3-1-1-1-11111-1-111-1-111-33-3300000000−ii−ii1-11-1−ii−iiii−i−iii−i−i−i−iii−i−iiii−ii−ii−ii−i000000000000
χ493-3-33-333-33-3-333-33-33-3-1-111-1-111-1-11111-1-13-3-3300000000i−i−ii-111-1i−i−ii−i−iiiii−i−i−i−iiiii−i−ii−i−iii−i−ii000000000000
χ503-3-33-333-33-3-333-33-33-3-1-111-1-111-1-11111-1-13-3-3300000000−iii−i-111-1−iii−iii−i−i−i−iiiii−i−i−i−iii−iii−i−iii−i000000000000
χ513-3-33-333-33-3-333-33-33-3-1-111-1-111-1-11111-1-1-333-300000000i−i−ii1-1-11i−i−ii−i−iiiii−i−iii−i−i−i−iii−iii−i−iii−i000000000000
χ523-3-33-333-33-3-333-33-33-3-1-111-1-111-1-11111-1-1-333-300000000−iii−i1-1-11−iii−iii−i−i−i−iii−i−iiiii−i−ii−i−iii−i−ii000000000000
χ536666666666-2-2-2-2-2-2-2-22-22-22-22-2-22-22-22-2200000000000022220000-2-2-2-2000000000000000000000000000000000000
χ546666666666-2-2-2-2-2-2-2-22-22-22-22-2-22-22-22-22000000000000-2-2-2-200002222000000000000000000000000000000000000
χ556666666666-2-2-2-2-2-2-2-2-22-22-22-222-22-22-22-200000000000000000000000000000000000000002222-2-2-2-2000000000000
χ566666666666-2-2-2-2-2-2-2-2-22-22-22-222-22-22-22-20000000000000000000000000000000000000000-2-2-2-22222000000000000
χ57666666-6-6-6-66666-6-6-6-6-22-22-22-22-22-22-22-22000000000000000000000000000000000000000000000000000000000000
χ58666666-6-6-6-6-2-2-2-2222222222222-2-2-2-2-2-2-2-20000000000000000000000002-22-22-22-20000000000000000000000000000
χ59666666-6-6-6-6-2-2-2-2222222222222-2-2-2-2-2-2-2-2000000000000000000000000-22-22-22-220000000000000000000000000000
χ60666666-6-6-6-6-2-2-2-22222-2-2-2-2-2-2-2-222222222000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ61666666-6-6-6-6-2-2-2-22222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ626666-6-66-6-6622-2-2-222-22-2-22-222-2-22-222-22-200000000000022-2-20000-2-222000000000000000000000000000000000000
χ636666-6-66-6-6622-2-2-222-22-2-22-222-2-22-222-22-2000000000000-2-222000022-2-2000000000000000000000000000000000000
χ646666-6-66-6-6622-2-2-222-2-222-22-2-222-22-2-22-22000000000000000000000000000000000000000022-2-2-2-222000000000000
χ656666-6-66-6-6622-2-2-222-2-222-22-2-222-22-2-22-220000000000000000000000000000000000000000-2-22222-2-2000000000000
χ666666-6-6-666-622-2-22-2-2222-2-2-2-222-2-2-2-222220000000000000000000000002-22-2-22-220000000000000000000000000000
χ676666-6-6-666-622-2-22-2-2222-2-2-2-222-2-2-2-22222000000000000000000000000-22-222-22-20000000000000000000000000000
χ686666-6-6-666-622-2-22-2-22-2-22222-2-22222-2-2-2-2000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ696666-6-6-666-622-2-22-2-22-2-22222-2-22222-2-2-2-200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ706666-6-6-666-6-6-666-666-6-222-22-2-22-22-222-22-2000000000000000000000000000000000000000000000000000000000000
χ716-6-666-666-6-6-22-22-2-2222-22-2-22-22-222-2-222-20000000000002i−2i2i−2i0000−2i2i−2i2i000000000000000000000000000000000000
χ726-6-666-666-6-6-22-22-2-2222-22-2-22-22-222-2-222-2000000000000−2i2i−2i2i00002i−2i2i−2i000000000000000000000000000000000000
χ736-6-666-666-6-6-22-22-2-222-22-222-22-22-2-222-2-2200000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ746-6-666-666-6-6-22-22-2-222-22-222-22-22-2-222-2-220000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ756-6-666-6-6-6666-66-6-6-666-22-222-22-2-222-2-222-2000000000000000000000000000000000000000000000000000000000000
χ766-6-666-6-6-666-22-2222-2-22222-2-2-2-2-2-222-2-2220000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ776-6-666-6-6-666-22-2222-2-22222-2-2-2-2-2-222-2-222000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ786-6-666-6-6-666-22-2222-2-2-2-2-2-2222222-2-222-2-2000000000000000000000000000000002-2-222-2-2200000000000000000000
χ796-6-666-6-6-666-22-2222-2-2-2-2-2-2222222-2-222-2-200000000000000000000000000000000-222-2-222-200000000000000000000
χ806-6-66-666-66-62-2-22-22-222-2-222-2-22-222-22-2-220000000000002i−2i−2i2i0000−2i2i2i−2i000000000000000000000000000000000000
χ816-6-66-666-66-62-2-22-22-222-2-222-2-22-222-22-2-22000000000000−2i2i2i−2i00002i−2i−2i2i000000000000000000000000000000000000
χ826-6-66-666-66-62-2-22-22-22-222-2-222-22-2-22-222-200000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ836-6-66-666-66-62-2-22-22-22-222-2-222-22-2-22-222-20000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ846-6-66-66-66-662-2-222-22-222-2-222-2-2-2-22222-2-20000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ856-6-66-66-66-662-2-222-22-222-2-222-2-2-2-22222-2-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ866-6-66-66-66-662-2-222-22-2-2-222-2-22222-2-2-2-222000000000000000000000000000000002-2-22-222-200000000000000000000
χ876-6-66-66-66-662-2-222-22-2-2-222-2-22222-2-2-2-22200000000000000000000000000000000-222-22-2-2200000000000000000000
χ886-6-66-66-66-66-666-6-66-66-222-2-222-2-222-22-2-22000000000000000000000000000000000000000000000000000000000000
χ891616-16-16000000000000000000000000000000000044-40000-4000000000000000000000000000000000000000000000000
χ901616-16-160000000000000000000000000000000000-2-22−2i32i3−2i32i32000000000000000000000000000000000000000000000000
χ911616-16-160000000000000000000000000000000000-2-222i3−2i32i3−2i32000000000000000000000000000000000000000000000000
χ9216-1616-1600000000000000000000000000000000004-440000-4000000000000000000000000000000000000000000000000
χ9316-1616-160000000000000000000000000000000000-22-2−2i32i32i3−2i32000000000000000000000000000000000000000000000000
χ9416-1616-160000000000000000000000000000000000-22-22i3−2i3−2i32i32000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).