Finite Group Databasebeta

← Group #72344078

Character table — Group #72344078

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size112222222666666668888888812121212121212121212121212121212161616162424242424242424323232323232323232323232323232323232323232323232323232323232
order12222224422222244222244442222222244444444336644444444666666666666666666121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ311111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ411111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111-1-1-1-111-1-1-1-1
χ511111111111111111-1-1-1-1-1-1-1-11111111111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32
χ611111111111111111-1-1-1-1-1-1-1-11111111111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32
χ711111-1-1-1-1111-1-11-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-111-1-1111-1-111-1-1-1-111-1-1-1-111-1-1
χ811111-1-1-1-1111-1-11-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i321111-1-1-1-1−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32
χ911111-1-1-1-1111-1-11-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i321111-1-1-1-1−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32
χ1011111-1-1-1-1111-1-11-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111111-1-1-1-111111-1-1-1-111-1-1-1-111-1-1-1-111
χ1111111-1-1-1-1111-1-11-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-1-1-1-11111−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32
χ1211111-1-1-1-1111-1-11-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-1-1-1-11111−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32
χ13111-1-111-1-11-1-1111-1-11-11-11-11-111-1-111-1-111-1-111-1-1111111-1-111-1-11-1-1111-11-11-1-1111-11-1-1-11-11-1-1-11-11-1
χ14111-1-111-1-11-1-1111-1-11-11-11-11-111-1-111-1-111-1-111-1-1−1+i32−1−i32−1+i32−1−i3211-1-111-1-1−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i321−i321−i32−1+i321−i32−1+i321−i321+i321+i32−1−i321+i32−1−i321+i32
χ15111-1-111-1-11-1-1111-1-11-11-11-11-111-1-111-1-111-1-111-1-1−1−i32−1+i32−1−i32−1+i3211-1-111-1-1−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i321+i321+i32−1−i321+i32−1−i321+i321−i321−i32−1+i321−i32−1+i321−i32
χ16111-1-111-1-11-1-1111-1-1-11-11-11-1111-1-111-1-111-1-111-1-11111-1-111-1-1111-1-111-11-111-1-111-11-11-1-1-11-11-1-1-11-11
χ17111-1-111-1-11-1-1111-1-1-11-11-11-1111-1-111-1-111-1-111-1-1−1+i32−1−i32−1+i32−1−i32-1-111-1-111−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321−i321−i321−i32−1+i321−i32−1+i321+i321+i321+i32−1−i321+i32−1−i32
χ18111-1-111-1-11-1-1111-1-1-11-11-11-1111-1-111-1-111-1-111-1-1−1−i32−1+i32−1−i32−1+i32-1-111-1-111−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i321+i321+i321+i32−1−i321+i32−1−i321−i321−i321−i32−1+i321−i32−1+i32
χ19111-1-1-1-1111-1-1-1-11111-1-111-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-11-1-111-1-1-1-11-1-11111-1-11111-1-11
χ20111-1-1-1-1111-1-1-1-11111-1-111-1-1111-1-1-1-11111-1-1-1-111−1+i32−1−i32−1+i32−1−i3211-1-1-1-111−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i321+i32−1−i32
χ21111-1-1-1-1111-1-1-1-11111-1-111-1-1111-1-1-1-11111-1-1-1-111−1−i32−1+i32−1−i32−1+i3211-1-1-1-111−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i32−1+i321−i321−i32−1+i32
χ22111-1-1-1-1111-1-1-1-1111-111-1-111-111-1-1-1-11111-1-1-1-1111111-1-11111-1-11-1-1-1-1-111-11-1-1-1-1-111-111-111-111-111-1
χ23111-1-1-1-1111-1-1-1-1111-111-1-111-111-1-1-1-11111-1-1-1-111−1+i32−1−i32−1+i32−1−i32-1-11111-1-1−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ24111-1-1-1-1111-1-1-1-1111-111-1-111-111-1-1-1-11111-1-1-1-111−1−i32−1+i32−1−i32−1+i32-1-11111-1-1−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i32
χ2511-11-11-11-1-11-11-111-1111-1-1-1-111-11-11-11-11-11-11-11-111111-11-11-11-1-11-11-1111-1-11-11-1111-11-1-1-1-111-1-1-1-11
χ2611-11-11-11-1-11-11-111-1111-1-1-1-111-11-11-11-11-11-11-11-1−1+i32−1−i32−1+i32−1−i321-11-11-11-11−i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i32−1+i321−i321−i321−i321−i32−1+i32−1−i321+i321+i321+i321+i32−1−i32
χ2711-11-11-11-1-11-11-111-1111-1-1-1-111-11-11-11-11-11-11-11-1−1−i32−1+i32−1−i32−1+i321-11-11-11-11+i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i32−1−i321+i321+i321+i321+i32−1−i32−1+i321−i321−i321−i321−i32−1+i32
χ2811-11-11-11-1-11-11-111-1-1-1-11111-11-11-11-11-11-11-11-11-11111-11-11-11-11-11-11-1-1-1-11-11-11-1-1-1-111-1111-11-1111-1
χ2911-11-11-11-1-11-11-111-1-1-1-11111-11-11-11-11-11-11-11-11-1−1+i32−1−i32−1+i32−1−i32-11-11-11-111−i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i321+i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i32−1+i321−i32−1+i32−1+i32−1+i321−i32−1−i321+i32−1−i32−1−i32−1−i321+i32
χ3011-11-11-11-1-11-11-111-1-1-1-11111-11-11-11-11-11-11-11-11-1−1−i32−1+i32−1−i32−1+i32-11-11-11-111+i32−1−i321+i32−1−i321+i321+i321+i321+i32−1−i321−i32−1+i321−i32−1+i321−i321−i321−i321−i32−1+i32−1−i321+i32−1−i32−1−i32−1−i321+i32−1+i321−i32−1+i32−1+i32−1+i321−i32
χ3111-11-1-11-11-11-1-111-1111-11-1-11-11-11-1-11-111-11-1-11-1111111-11-1-11-11-11-1-1111-11-11-1-1111-11-11-1-11-1-11-1-11-1
χ3211-11-1-11-11-11-1-111-1111-11-1-11-11-11-1-11-111-11-1-11-11−1+i32−1−i32−1+i32−1−i321-11-1-11-111−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321−i32−1+i321−i321−i32−1+i321−i321+i32−1−i321+i321+i32−1−i321+i32
χ3311-11-1-11-11-11-1-111-1111-11-1-11-11-11-1-11-111-11-1-11-11−1−i32−1+i32−1−i32−1+i321-11-1-11-111+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321+i32−1−i321+i321+i32−1−i321+i321−i32−1+i321−i321−i32−1+i321−i32
χ3411-11-1-11-11-11-1-111-11-1-11-111-111-11-1-11-111-11-1-11-111111-11-111-11-1-11-1-11-1-11-1-11-1-11-1-11-1-1111-11-1111-11
χ3511-11-1-11-11-11-1-111-11-1-11-111-111-11-1-11-111-11-1-11-11−1+i32−1−i32−1+i32−1−i32-11-111-11-11−i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321−i32−1+i32−1+i32−1+i321−i32−1+i321+i32−1−i32−1−i32−1−i321+i32−1−i32
χ3611-11-1-11-11-11-1-111-11-1-11-111-111-11-1-11-111-11-1-11-11−1−i32−1+i32−1−i32−1+i32-11-111-11-11+i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321+i32−1−i32−1−i32−1−i321+i32−1−i321−i32−1+i32−1+i32−1+i321−i32−1+i32
χ3711-1-111-1-11-1-111-11-111-111-11-1-11-1-111-1-111-1-111-1-1111111-1-111-1-11-1-111-11-111-1-111-11-111-11-11-1-1-11-11-1-1
χ3811-1-111-1-11-1-111-11-111-111-11-1-11-1-111-1-111-1-111-1-11−1+i32−1−i32−1+i32−1−i321-1-111-1-111−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321−i32−1+i321−i32−1+i321−i321−i321+i32−1−i321+i32−1−i321+i321+i32
χ3911-1-111-1-11-1-111-11-111-111-11-1-11-1-111-1-111-1-111-1-11−1−i32−1+i32−1−i32−1+i321-1-111-1-111+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321+i32−1−i321+i32−1−i321+i321+i321−i32−1+i321−i32−1+i321−i321−i32
χ4011-1-111-1-11-1-111-11-11-11-1-11-1111-1-111-1-111-1-111-1-111111-111-1-111-1-1-111-1-11-1-1-1-111-1-11-1-1-111-111-111-111
χ4111-1-111-1-11-1-111-11-11-11-1-11-1111-1-111-1-111-1-111-1-11−1+i32−1−i32−1+i32−1−i32-111-1-111-11−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i321−i32−1+i32−1+i321−i32−1+i32−1+i321+i32−1−i32−1−i321+i32−1−i32−1−i32
χ4211-1-111-1-11-1-111-11-11-11-1-11-1111-1-111-1-111-1-111-1-11−1−i32−1+i32−1−i32−1+i32-111-1-111-11+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i321+i32−1−i32−1−i321+i32−1−i32−1−i321−i32−1+i32−1+i321−i32−1+i32−1+i32
χ4311-1-11-111-1-1-11-1111-11-1-1-1-11111-1-11-111-11-1-11-111-111111-1-11-111-1-1-11-111-1-1-1-1-11-111-1-1-11-1-11111-1-1111
χ4411-1-11-111-1-1-11-1111-11-1-1-1-11111-1-11-111-11-1-11-111-1−1+i32−1−i32−1+i32−1−i321-1-11-111-11−i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1−i321+i321+i32−1−i32−1−i32−1−i32
χ4511-1-11-111-1-1-11-1111-11-1-1-1-11111-1-11-111-11-1-11-111-1−1−i32−1+i32−1−i32−1+i321-1-11-111-11+i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1+i321−i321−i32−1+i32−1+i32−1+i32
χ4611-1-11-111-1-1-11-1111-1-11111-1-1-11-1-11-111-11-1-11-111-11111-111-11-1-11-1-11-11-1111-1-11-11-11111-11-1-1-11-11-1-1-1
χ4711-1-11-111-1-1-11-1111-1-11111-1-1-11-1-11-111-11-1-11-111-1−1+i32−1−i32−1+i32−1−i32-111-11-1-111−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i32−1+i321−i32−1+i321−i321−i321−i32−1−i321+i32−1−i321+i321+i321+i32
χ4811-1-11-111-1-1-11-1111-1-11111-1-1-11-1-11-111-11-1-11-111-1−1−i32−1+i32−1−i32−1+i32-111-11-1-111+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32−1−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32−1+i32−1−i321+i32−1−i321+i321+i321+i32−1+i321−i32−1+i321−i321−i321−i32
χ493333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1000000000000000000000000000000
χ5033333333333333333-3-3-3-3-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000011111111000000000000000000000000000000
χ5133333-3-3-3-3333-3-33-3-333-3-333-3-3-1-1-1-11111-1-1-1-111110000-1-1-1-11111000000000000000000000000000000
χ5233333-3-3-3-3333-3-33-3-3-3-333-3-333-1-1-1-11111-1-1-1-1111100001111-1-1-1-1000000000000000000000000000000
χ53333-3-333-3-33-3-3333-3-33-33-33-33-3-1-111-1-111-1-111-1-1110000-1-111-1-111000000000000000000000000000000
χ54333-3-333-3-33-3-3333-3-3-33-33-33-33-1-111-1-111-1-111-1-111000011-1-111-1-1000000000000000000000000000000
χ55333-3-3-3-3333-3-3-3-33333-3-333-3-33-1-11111-1-1-1-11111-1-10000-1-11111-1-1000000000000000000000000000000
χ56333-3-3-3-3333-3-3-3-3333-333-3-333-3-1-11111-1-1-1-11111-1-1000011-1-1-1-111000000000000000000000000000000
χ5733-33-33-33-3-33-33-333-3333-3-3-3-33-11-11-11-11-11-11-11-110000-11-11-11-11000000000000000000000000000000
χ5833-33-33-33-3-33-33-333-3-3-3-33333-3-11-11-11-11-11-11-11-1100001-11-11-11-1000000000000000000000000000000
χ5933-33-3-33-33-33-3-333-3333-33-3-33-3-11-111-11-1-11-111-11-10000-11-111-11-1000000000000000000000000000000
χ6033-33-3-33-33-33-3-333-33-3-33-333-33-11-111-11-1-11-111-11-100001-11-1-11-11000000000000000000000000000000
χ6133-3-333-3-33-3-333-33-333-333-33-3-3-111-1-111-1-111-1-111-10000-111-1-111-1000000000000000000000000000000
χ6233-3-333-3-33-3-333-33-33-33-3-33-333-111-1-111-1-111-1-111-100001-1-111-1-11000000000000000000000000000000
χ6333-3-33-333-3-3-33-3333-33-3-3-3-3333-111-11-1-11-111-11-1-110000-111-11-1-11000000000000000000000000000000
χ6433-3-33-333-3-3-33-3333-3-33333-3-3-3-111-11-1-11-111-11-1-1100001-1-11-111-1000000000000000000000000000000
χ65666666666-2-2-2-2-2-2-2-200000000222222-2-2-2-2-2-2-2-222000000000000000000000000000000000000000000
χ66666666666-2-2-2-2-2-2-2-200000000-2-2-2-2-2-222222222-2-2000000000000000000000000000000000000000000
χ6766666-6-6-6-6-2-2-222-222000000002222-2-222-2-2-2-222-2-2000000000000000000000000000000000000000000
χ6866666-6-6-6-6-2-2-222-22200000000-2-2-2-222-2-22222-2-222000000000000000000000000000000000000000000
χ69666-6-666-6-6-222-2-2-2220000000022-2-22222-2-222-2-2-2-2000000000000000000000000000000000000000000
χ70666-6-666-6-6-222-2-2-22200000000-2-222-2-2-2-222-2-22222000000000000000000000000000000000000000000
χ71666-6-6-6-666-22222-2-2-20000000022-2-2-2-2-2-2-2-2222222000000000000000000000000000000000000000000
χ72666-6-6-6-666-22222-2-2-200000000-2-222222222-2-2-2-2-2-2000000000000000000000000000000000000000000
χ7366-66-66-66-62-22-22-2-22000000002-22-22-2-22-22-22-222-2000000000000000000000000000000000000000000
χ7466-66-66-66-62-22-22-2-2200000000-22-22-222-22-22-22-2-22000000000000000000000000000000000000000000
χ7566-66-6-66-662-222-2-22-2000000002-22-2-222-2-22-222-2-22000000000000000000000000000000000000000000
χ7666-66-6-66-662-222-2-22-200000000-22-222-2-222-22-2-222-2000000000000000000000000000000000000000000
χ7766-6-666-6-6622-2-22-22-2000000002-2-222-22-2-222-2-22-22000000000000000000000000000000000000000000
χ7866-6-666-6-6622-2-22-22-200000000-222-2-22-222-2-222-22-2000000000000000000000000000000000000000000
χ7966-6-66-666-622-22-2-2-22000000002-2-22-22-22-222-22-22-2000000000000000000000000000000000000000000
χ8066-6-66-666-622-22-2-2-2200000000-222-22-22-22-2-22-22-22000000000000000000000000000000000000000000
χ8116-1600000000000000000000000000000000000000044-4-400000000000000000000000000000000000000
χ8216-16000000000000000000000000000000000000000−2+2i3−2−2i32−2i32+2i300000000000000000000000000000000000000
χ8316-16000000000000000000000000000000000000000−2−2i3−2+2i32+2i32−2i300000000000000000000000000000000000000

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