Finite Group Databasebeta

← Group #72240029

Character table — Group #72240029

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111133333333333333333333121212121212121212121212121212122424242424242424242424242424242424242424242424242424242424242424256256256256256256256256
order12222222222222222222222244444444444444444444444444444444444444444444444433666666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ3111111111111111111111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ422-2-2222222222-2-2-2-2-2-2-22-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000000000000-1-111-111-1
χ522-2-2222222222-2-2-2-2-2-2-22-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32
χ622-2-2222222222-2-2-2-2-2-2-22-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32
χ73333333333333333333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ8333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ9333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ10333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133333333-1-1-1-1-1-1-1-100000000
χ11333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333333300000000
χ12333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-11111−1+2i−1+2i−1−2i−1−2i1111−1+2i−1+2i−1−2i−1−2i1111−1+2i−1+2i−1−2i−1−2i33-1-1-1-1-1-11111−1+2i−1+2i−1−2i−1−2i1111−1+2i−1+2i−1−2i−1−2i00000000
χ13333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-11111−1+2i−1+2i−1−2i−1−2i1111−1+2i−1+2i−1−2i−1−2i1111−1−2i−1−2i−1+2i−1+2i-1-133-1-1-1-1−1+2i−1+2i−1−2i−1−2i1111−1+2i−1+2i−1−2i−1−2i111100000000
χ14333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-11111−1+2i−1+2i−1−2i−1−2i1111−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i1111-1-1-1-133-1-11111−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i111100000000
χ15333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-11111−1+2i−1+2i−1−2i−1−2i1111−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i1111-1-1-1-1-1-133−1−2i−1−2i−1+2i−1+2i11111111−1−2i−1−2i−1+2i−1+2i00000000
χ16333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-11111−1−2i−1−2i−1+2i−1+2i1111−1−2i−1−2i−1+2i−1+2i1111−1+2i−1+2i−1−2i−1−2i-1-133-1-1-1-1−1−2i−1−2i−1+2i−1+2i1111−1−2i−1−2i−1+2i−1+2i111100000000
χ17333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-11111−1−2i−1−2i−1+2i−1+2i1111−1−2i−1−2i−1+2i−1+2i1111−1−2i−1−2i−1+2i−1+2i33-1-1-1-1-1-11111−1−2i−1−2i−1+2i−1+2i1111−1−2i−1−2i−1+2i−1+2i00000000
χ18333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-11111−1−2i−1−2i−1+2i−1+2i1111−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i1111-1-1-1-1-1-133−1+2i−1+2i−1−2i−1−2i11111111−1+2i−1+2i−1−2i−1−2i00000000
χ19333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-11111−1−2i−1−2i−1+2i−1+2i1111−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i1111-1-1-1-133-1-11111−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i111100000000
χ20333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-1−1+2i−1+2i−1−2i−1−2i1111−1+2i−1+2i−1−2i−1−2i11111111−1+2i−1+2i−1−2i−1−2i-1-1-1-133-1-1−1+2i−1+2i−1−2i−1−2i11111111−1−2i−1−2i−1+2i−1+2i00000000
χ21333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-1−1+2i−1+2i−1−2i−1−2i1111−1+2i−1+2i−1−2i−1−2i11111111−1−2i−1−2i−1+2i−1+2i-1-1-1-1-1-1331111−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i111100000000
χ22333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-1−1+2i−1+2i−1−2i−1−2i1111−1+2i−1+2i−1−2i−1−2i1111−1+2i−1+2i−1−2i−1−2i111133-1-1-1-1-1-1−1−2i−1−2i−1+2i−1+2i1111−1+2i−1+2i−1−2i−1−2i111100000000
χ23333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-1−1+2i−1+2i−1−2i−1−2i1111−1+2i−1+2i−1−2i−1−2i1111−1−2i−1−2i−1+2i−1+2i1111-1-133-1-1-1-11111−1−2i−1−2i−1+2i−1+2i1111−1+2i−1+2i−1−2i−1−2i00000000
χ24333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-1−1−2i−1−2i−1+2i−1+2i1111−1−2i−1−2i−1+2i−1+2i11111111−1+2i−1+2i−1−2i−1−2i-1-1-1-1-1-1331111−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i111100000000
χ25333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-1−1−2i−1−2i−1+2i−1+2i1111−1−2i−1−2i−1+2i−1+2i11111111−1−2i−1−2i−1+2i−1+2i-1-1-1-133-1-1−1−2i−1−2i−1+2i−1+2i11111111−1+2i−1+2i−1−2i−1−2i00000000
χ26333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-1−1−2i−1−2i−1+2i−1+2i1111−1−2i−1−2i−1+2i−1+2i1111−1+2i−1+2i−1−2i−1−2i1111-1-133-1-1-1-11111−1+2i−1+2i−1−2i−1−2i1111−1−2i−1−2i−1+2i−1+2i00000000
χ27333333-1-1-1-1-1-1-13-1-1-1-1-1-1-13-1-1−1−2i−1−2i−1+2i−1+2i1111−1−2i−1−2i−1+2i−1+2i1111−1−2i−1−2i−1+2i−1+2i111133-1-1-1-1-1-1−1+2i−1+2i−1−2i−1−2i1111−1−2i−1−2i−1+2i−1+2i111100000000
χ284-44-44-4444-4-4-4-44444-4-4-44-4-44000000000000000000000000000000000000000000000000111-1-11-1-1
χ294-44-44-4444-4-4-4-44444-4-4-44-4-44000000000000000000000000000000000000000000000000−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ304-44-44-4444-4-4-4-44444-4-4-44-4-44000000000000000000000000000000000000000000000000−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ314-4-444-4444-4-4-4-4-4-4-4-4444444-400000000000000000000000000000000000000000000000011-11-1-11-1
χ324-4-444-4444-4-4-4-4-4-4-4-4444444-4000000000000000000000000000000000000000000000000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ334-4-444-4444-4-4-4-4-4-4-4-4444444-4000000000000000000000000000000000000000000000000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ3466-6-6666666666-6-6-6-6-6-6-66-6-6-6-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ3566-6-666-2-2-2-2-2-2-2-6222222-2-6222222−2+4i−2+4i−2−4i−2−4i-2-2-2-22−4i2−4i2+4i2+4i0000000000000000000000000000000000000000
χ3666-6-666-2-2-2-2-2-2-2-6222222-2-6222222−2−4i−2−4i−2+4i−2+4i-2-2-2-22+4i2+4i2−4i2−4i0000000000000000000000000000000000000000
χ3766-6-666-2-2-2-2-2-2-2-6222222-2-622−2+4i−2+4i−2−4i−2−4i22222−4i2−4i2+4i2+4i-2-2-2-20000000000000000000000000000000000000000
χ3866-6-666-2-2-2-2-2-2-2-6222222-2-622−2−4i−2−4i−2+4i−2+4i22222+4i2+4i2−4i2−4i-2-2-2-20000000000000000000000000000000000000000
χ396-66-6-226-2-2222-6-26-2-222-6-222-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000002-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000
χ406-66-6-226-2-2222-6-26-2-222-6-222-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000-22-22-22-22−2i2i−2i2i−2i2i−2i2i00000000
χ416-66-6-226-2-2222-6-26-2-222-6-222-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000002-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000
χ426-66-6-226-2-2222-6-26-2-222-6-222-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000-22-22-22-222i−2i2i−2i2i−2i2i−2i00000000
χ436-66-6-22-26-222-62-2-26-22-62-222-22i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000002i−2i−2i2i2i−2i−2i2i-222-2-222-200000000
χ446-66-6-22-26-222-62-2-26-22-62-222-22i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000000000−2i2i2i−2i−2i2i2i−2i2-2-222-2-2200000000
χ456-66-6-22-26-222-62-2-26-22-62-222-2−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000002i−2i−2i2i2i−2i−2i2i2-2-222-2-2200000000
χ466-66-6-22-26-222-62-2-26-22-62-222-2−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i0000000000000000−2i2i2i−2i−2i2i2i−2i-222-2-222-200000000
χ476-66-6-22-2-262-622-2-2-2-2-622-22262-2-222-2-222-2-222-2-2200000000000000002-22-2-22-22-222-22-2-2200000000
χ486-66-6-22-2-262-622-2-2-2-2-622-22262-2-222-2-222-2-222-2-220000000000000000-22-222-22-22-2-22-222-200000000
χ496-66-6-22-2-262-622-2-2-2-2-622-2226-222-2-222-2-222-2-222-200000000000000002-22-2-22-222-2-22-222-200000000
χ506-66-6-22-2-262-622-2-2-2-2-622-2226-222-2-222-2-222-2-222-20000000000000000-22-222-22-2-222-22-2-2200000000
χ516-66-6-22-2-2-2-6222-2-2-2622262-6-22-2-22-222-22-2-22-222-200000000000000002i−2i−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000
χ526-66-6-22-2-2-2-6222-2-2-2622262-6-22-2-22-222-22-2-22-222-20000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000
χ536-66-6-22-2-2-2-6222-2-2-2622262-6-2-222-22-2-22-222-22-2-2200000000000000002i−2i−2i2i−2i2i2i−2i2i−2i2i−2i−2i2i−2i2i00000000
χ546-66-6-22-2-2-2-6222-2-2-2622262-6-2-222-22-2-22-222-22-2-220000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i−2i2i2i−2i2i−2i00000000
χ556-6-66-226-2-2222-62-622-2-26-2-2-222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i2-22-22-22-2000000000000000000000000
χ566-6-66-226-2-2222-62-622-2-26-2-2-222i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i-22-22-22-22000000000000000000000000
χ576-6-66-226-2-2222-62-622-2-26-2-2-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i-22-22-22-22000000000000000000000000
χ586-6-66-226-2-2222-62-622-2-26-2-2-22−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2-22-22-22-2000000000000000000000000
χ596-6-66-22-26-222-6222-62-26-2-2-2-222i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i2-22-2-22-22000000000000000000000000
χ606-6-66-22-26-222-6222-62-26-2-2-2-222i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i-22-222-22-2000000000000000000000000
χ616-6-66-22-26-222-6222-62-26-2-2-2-22−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i-22-222-22-2000000000000000000000000
χ626-6-66-22-26-222-6222-62-26-2-2-2-22−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2-22-2-22-22000000000000000000000000
χ636-6-66-22-2-262-62222226-2-2-2-2-2-62-2-222-2-22-222-2-222-22-2-222-2-222-2-222-2-22000000000000000000000000
χ646-6-66-22-2-262-62222226-2-2-2-2-2-62-2-222-2-22-222-2-222-2-222-2-222-2-222-2-222-2000000000000000000000000
χ656-6-66-22-2-262-62222226-2-2-2-2-2-6-222-2-222-22-2-222-2-222-2-222-2-22-222-2-222-2000000000000000000000000
χ666-6-66-22-2-262-62222226-2-2-2-2-2-6-222-2-222-22-2-222-2-22-222-2-222-22-2-222-2-22000000000000000000000000
χ676-6-66-22-2-2-2-6222222-6-2-2-26-2622-2-22-222-2-222-22-2-222-2-22-222-22-2-22-222-2000000000000000000000000
χ686-6-66-22-2-2-2-6222222-6-2-2-26-2622-2-22-222-2-222-22-2-22-222-22-2-22-222-22-2-22000000000000000000000000
χ696-6-66-22-2-2-2-6222222-6-2-2-26-262-222-22-2-222-2-22-222-22-2-22-222-2-222-22-2-22000000000000000000000000
χ706-6-66-22-2-2-2-6222222-6-2-2-26-262-222-22-2-222-2-22-222-2-222-22-2-222-2-22-222-2000000000000000000000000
χ7112121212-4-412-4-4-4-4-412-412-4-4-4-412-4-4-4-400000000000000000000000000000000000000000000000000000000
χ7212121212-4-4-412-4-4-412-4-4-412-4-412-4-4-4-4-400000000000000000000000000000000000000000000000000000000
χ7312121212-4-4-4-412-412-4-4-4-4-4-412-4-4-4-4-41200000000000000000000000000000000000000000000000000000000
χ7412121212-4-4-4-4-412-4-4-4-4-4-412-4-4-412-412-400000000000000000000000000000000000000000000000000000000
χ751212-12-12-4-412-4-4-4-4-4124-124444-12-444400000000000000000000000000000000000000000000000000000000
χ761212-12-12-4-4-412-4-4-412-444-1244-124-444400000000000000000000000000000000000000000000000000000000
χ771212-12-12-4-4-4-412-412-4-44444-1244-444-1200000000000000000000000000000000000000000000000000000000
χ781212-12-12-4-4-4-4-412-4-4-4444-12444124-12400000000000000000000000000000000000000000000000000000000
χ7912-1212-1212-12-4-4-4444412-4-4-4444-4-124-400000000000000000000000000000000000000000000000000000000
χ8012-12-121212-12-4-4-44444-12444-4-4-4-412-4400000000000000000000000000000000000000000000000000000000

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