Finite Group Databasebeta

← Group #13057509

Character table — Group #13057509

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size11222444444667777121212141414141414141414141414141414141414141414141414242424242424282828282828282828282828282828282828282828282828282828
order12244222488714336614282822446666668812121212121212122424242414141428565624446666666681212121212121212242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-111-1-1-1-1-1-11111-1-1
χ31111111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321−1−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
χ41111111111111−1−i32−1+i32−1−i32−1+i32111-1-1-1-1−1−i32−1+i321+i321+i321−i321−i32-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32111111-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i32-1−1−i32−1+i321+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32
χ51111111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−1+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
χ61111111111111−1+i32−1−i32−1+i32−1−i32111-1-1-1-1−1+i32−1−i321−i321−i321+i321+i32-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32111111-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i32-1−1+i32−1−i321−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32
χ71111111-1-1-1-11111111111111111111-1-111111111-1-1-1-111-1-1-1-111-1-111-111-111-1-1-11-1-11-1-1-1-1-1-1-1-1
χ81111111-1-1-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-111-1-1-11-1-1-111-111-1-1-1-111
χ91111111-1-1-1-111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i3211-1-1-1-111-1-1−1−i32−1−i321+i32−1+i32−1+i321−i32−1−i32−1+i32-11+i321−i32−1−i321+i321+i32−1+i321−i321−i321+i321+i321−i321−i321+i321−i32
χ101111111-1-1-1-111−1−i32−1+i32−1−i32−1+i32111-1-1-1-1−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-1-1-111−1−i32−1−i321+i32−1+i32−1+i321−i321+i321−i3211+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i32
χ111111111-1-1-1-111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i3211-1-1-1-111-1-1−1+i32−1+i321−i32−1−i32−1−i321+i32−1+i32−1−i32-11−i321+i32−1+i321−i321−i32−1−i321+i321+i321−i321−i321+i321+i321−i321+i32
χ121111111-1-1-1-111−1+i32−1−i32−1+i32−1−i32111-1-1-1-1−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-1-1-111−1+i32−1+i321−i32−1−i32−1−i321+i321−i321+i3211−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i32
χ1311111-1-111-1-11111111111111111111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-11-1-11-1-1-111-111-111-1-1-1-1-1-1
χ1411111-1-111-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-11-1-11111111-1-11-1-1-1-1-1-111
χ1511111-1-111-1-111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1-111-1-1-1-1111+i321+i32−1−i321−i321−i32−1+i321+i321−i32-1−1−i32−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i321+i321+i321−i321−i321+i321−i32
χ1611111-1-111-1-111−1−i32−1+i32−1−i32−1+i32111-1-1-1-1−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-1-111-1-11+i321+i32−1−i321−i321−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i321+i321+i321−i321−i32−1−i32−1+i32
χ1711111-1-111-1-111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1-111-1-1-1-1111−i321−i32−1+i321+i321+i32−1−i321−i321+i32-1−1+i32−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i321−i321−i321+i321+i321−i321+i32
χ1811111-1-111-1-111−1+i32−1−i32−1+i32−1−i32111-1-1-1-1−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-1-111-1-11−i321−i32−1+i321+i321+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i321−i321−i321+i321+i32−1+i32−1−i32
χ1911111-1-1-1-111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111
χ2011111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-11111111111-1-1
χ2111111-1-1-1-11111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-111-1-1-1-11+i321+i321+i321−i321−i321−i321+i321−i3211+i321−i321+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32
χ2211111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32111-1-1-1-1−1−i32−1+i321+i321+i321−i321−i32-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32-1-1-1-11111111+i321+i321+i321−i321−i321−i32−1−i32−1+i32-11+i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32
χ2311111-1-1-1-11111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-111-1-1-1-11−i321−i321−i321+i321+i321+i321−i321+i3211−i321+i321−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32
χ2411111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32111-1-1-1-1−1+i32−1−i321−i321−i321+i321+i32-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32-1-1-1-11111111−i321−i321−i321+i321+i321+i32−1+i32−1−i32-11−i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32
χ2511-1-111-11-11-1111111-1-111-11-1-1-11-11-111-1-11-11-11111111-11-11-1-111-11-111-11-1-1-1-1-111-111-11-11-1-1-1
χ2611-1-111-11-11-1111111-1-11-11-11-1-1-11-11-1-1-1-1-11-1111-1-1-1-11-11-11-11-1-111-111-11111-1-1-1-11-1-111-11-111
χ2711-1-111-11-11-111−1−i32−1+i32−1−i32−1+i32-1-111-11-11+i321−i32−1−i321+i32−1+i321−i32111+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-11-11-1-111-1−1−i321+i32−1−i32−1+i321−i32−1+i321+i321−i32-11+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1−i321+i32−1+i321−i321+i321−i32
χ2811-1-111-11-11-111−1−i32−1+i32−1−i32−1+i32-1-11-11-111+i321−i321+i32−1−i321−i32−1+i32-1-11+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-11-11-11-1-11−1−i321+i32−1−i32−1+i321−i32−1+i32−1−i32−1+i3211+i321−i321+i321+i32−1−i321−i321−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i32
χ2911-1-111-11-11-111−1+i32−1−i32−1+i32−1−i32-1-111-11-11−i321+i32−1+i321−i32−1−i321+i32111−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-11-11-1-111-1−1+i321−i32−1+i32−1−i321+i32−1−i321−i321+i32-11−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1+i321−i32−1−i321+i321−i321+i32
χ3011-1-111-11-11-111−1+i32−1−i32−1+i32−1−i32-1-11-11-111−i321+i321−i32−1+i321+i32−1−i32-1-11−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321-11-11-11-1-11−1+i321−i32−1+i32−1−i321+i32−1−i32−1+i32−1−i3211−i321+i321−i321−i32−1+i321+i321+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i32
χ3111-1-111-1-11-11111111-1-111-11-1-1-11-11-1-1-1-1-11-11-111-1-1-1-11-1-11-11-11-111-1-11-1-1-1-11111-111-11-11-1111
χ3211-1-111-1-11-11111111-1-11-11-11-1-1-11-1111-1-1-11-111111111-1-11-111-11-11-1-11-1-111-111-11-1-11-1-11-11-1-1
χ3311-1-111-1-11-1111−1−i32−1+i32−1−i32−1+i32-1-111-11-11+i321−i32−1−i321+i32−1+i321−i32-1-11+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321+i321−i321−i321-1-11-11-11-11−1−i321+i321+i32−1+i321−i321−i321+i321−i321−1−i32−1+i32−1−i321+i32−1−i32−1+i321−i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1+i32
χ3411-1-111-1-11-1111−1−i32−1+i32−1−i32−1+i32-1-11-11-111+i321−i321+i32−1−i321−i32−1+i32111+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-11-111-11-1−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i32-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321−i32−1+i321+i321−i32
χ3511-1-111-1-11-1111−1+i32−1−i32−1+i32−1−i32-1-111-11-11−i321+i32−1+i321−i32−1−i321+i32-1-11−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321−i321+i321+i321-1-11-11-11-11−1+i321−i321−i32−1−i321+i321+i321−i321+i321−1+i32−1−i32−1+i321−i32−1+i32−1−i321+i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1−i32
χ3611-1-111-1-11-1111−1+i32−1−i32−1+i32−1−i32-1-11-11-111−i321+i321−i32−1+i321+i32−1−i32111−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-11-111-11-1−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i32-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321+i32−1−i321−i321+i32
χ3711-1-11-111-1-11111111-1-111-11-1-1-11-11-1-1-1-1-11-11-111-1-1-1-1-111-1-111-11-1-111-111111-1-1-11-1-11-1-11-1111
χ3811-1-11-111-1-11111111-1-11-11-11-1-1-11-1111-1-1-11-11111111-111-1-11-11-11-111-111-1-1-1-1-11-111-11-11-11-1-1
χ3911-1-11-111-1-1111−1−i32−1+i32−1−i32−1+i32-1-111-11-11+i321−i32−1−i321+i32−1+i321−i32-1-11+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321+i321−i321−i32-111-1-111-11-11+i32−1−i32−1−i321−i32−1+i32−1+i32−1−i32−1+i3211+i321−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i32
χ4011-1-11-111-1-1111−1−i32−1+i32−1−i32−1+i32-1-11-11-111+i321−i321+i32−1−i321−i32−1+i32111+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-111-1-11-11-111+i32−1−i32−1−i321−i32−1+i32−1+i321+i321−i32-11+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i321+i32−1−i321−i32−1+i321+i321−i32
χ4111-1-11-111-1-1111−1+i32−1−i32−1+i32−1−i32-1-111-11-11−i321+i32−1+i321−i32−1−i321+i32-1-11−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321−i321+i321+i32-111-1-111-11-11−i32−1+i32−1+i321+i32−1−i32−1−i32−1+i32−1−i3211−i321+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i32
χ4211-1-11-111-1-1111−1+i32−1−i32−1+i32−1−i32-1-11-11-111−i321+i321−i32−1+i321+i32−1−i32111−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-111-1-11-11-111−i32−1+i32−1+i321+i32−1−i32−1−i321−i321+i32-11−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i321−i32−1+i321+i32−1−i321−i321+i32
χ4311-1-11-11-111-1111111-1-111-11-1-1-11-11-111-1-11-11-1111111-11-111-11-1-11-11-1-11-111-111-1-11-1-111-11-1-1-1
χ4411-1-11-11-111-1111111-1-11-11-11-1-1-11-11-1-1-1-1-11-1111-1-1-1-1-11-111-1-111-1-11-1-11-1-1-111111-111-11-11-111
χ4511-1-11-11-111-111−1−i32−1+i32−1−i32−1+i32-1-111-11-11+i321−i32−1−i321+i32−1+i321−i32111+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-111-11-1-111+i32−1−i321+i321−i32−1+i321−i32−1−i32−1+i32-1−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32
χ4611-1-11-11-111-111−1−i32−1+i32−1−i32−1+i32-1-11-11-111+i321−i321+i32−1−i321−i32−1+i32-1-11+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-111-1-111-11+i32−1−i321+i321−i32−1+i321−i321+i321−i321−1−i32−1+i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32
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χ4811-1-11-11-111-111−1+i32−1−i32−1+i32−1−i32-1-11-11-111−i321+i321−i32−1+i321+i32−1−i32-1-11−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-111-1-111-11−i32−1+i321−i321+i32−1−i321+i321−i321+i321−1+i32−1−i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32
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χ5922-22-200000022−1+i3−1−i3−1+i3−1−i3-22-222-2-21−i31+i3−1+i3−1+i3−1−i3−1−i300−1+i3−1−i31−i31−i31+i31+i31−i31+i30000000000000000000000000000000000000
χ6022-22-200000022−1+i3−1−i3−1+i3−1−i3-22-2-2-2221−i31+i31−i31−i31+i31+i300−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i31+i30000000000000000000000000000000000000
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χ634-40000000004-4−2−2i3−2+2i32+2i32−2i30000000000000−2i22i2000000002ζ7+2ζ13−2ζ7−2ζ132ζ5+2ζ23−2ζ5−2ζ23000000000000000000000000000000000
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χ654-40000000004-4−2+2i3−2−2i32−2i32+2i30000000000000−2i22i2000000002ζ5+2ζ23−2ζ5−2ζ232ζ7+2ζ13−2ζ7−2ζ13000000000000000000000000000000000
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χ75121212-12-12000000-2-20000-222000000000000000000000000000000000000000000000000000000000
χ761212-1212-12000000-2-200002-22000000000000000000000000000000000000000000000000000000000
χ7724-24000000000-440000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.