Finite Group Databasebeta

← Group #72266658

Character table — Group #72266658

Order 12288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
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χ7216-16-1616−16i16i16i−16i8-8-88−8i8i8i−8i00000000000000000000000000000000000011-111-1-11-111-1-11-1-1i−i−iii−i−iii−i−iii−i−ii
χ7316-16-1616−16i16i16i−16i8-8-88−8i8i8i−8i000000000000000000000000000000000000−1−i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i321+i321−i32ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14
χ7416-16-1616−16i16i16i−16i8-8-88−8i8i8i−8i000000000000000000000000000000000000−1+i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i321−i321+i32ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22
χ75242424242424242400000000-8-8-8-800000044-4-4000000000000000000000000000000000000000000000000000000
χ76242424242424242400000000-8-8-8-8000000-4-444000000000000000000000000000000000000000000000000000000
χ7724242424-24-24-24-2400000000-8-8880000004-4-44000000000000000000000000000000000000000000000000000000
χ7824242424-24-24-24-2400000000-8-888000000-444-4000000000000000000000000000000000000000000000000000000
χ792424-24-2424-2424-241212-12-1212-1212-1200000000000000-2-222-2-2220000000000000000000000000000000000000000000000
χ802424-24-24-2424-24241212-12-12-1212-121200000000000000-2-22222-2-20000000000000000000000000000000000000000000000
χ8124-2424-2424i24i−24i−24i00000000-88−8i8i-88−8i8i000000000000000000000000000000000000000000000000000000000000
χ8224-2424-24−24i−24i24i24i00000000-888i−8i-888i−8i000000000000000000000000000000000000000000000000000000000000
χ8324-24-242424i−24i−24i24i-121212-12−12i12i12i−12i00000000000000-22-22−2i2i−2i2i0000000000000000000000000000000000000000000000
χ8424-24-2424−24i24i24i−24i-121212-1212i−12i−12i12i00000000000000-22-222i−2i2i−2i0000000000000000000000000000000000000000000000

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