Finite Group Databasebeta

← Group #72276706

Character table — Group #72276706

Order 3600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45
size12242525254850505050505050505050505050505050505050505050505050505050505050505090360450450450
order13524415333666688121212121212121224242424242424242424242424242424210488
χ1111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1
χ311111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1
χ411111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111-1-111111111i−i-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1i−i
χ61111-1-111111111i−i-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-11−ii
χ71111-1-111111111−ii-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1−ii
χ81111-1-111111111−ii-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-11i−i
χ92222222-1-1-12-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000
χ102222222-1-1-12-1-1-1-2-222-1-1-1-1-1-1-2-2111111-2-211111100000
χ112222-2-22-1-1-12-1-1-12i−2i-2-21111112i2i−i−i−i−i−i−i−2i−2iiiiiii00000
χ122222-2-22-1-1-12-1-1-1−2i2i-2-2111111−2i−2iiiiiii2i2i−i−i−i−i−i−i00000
χ13222-22i−2i2222-2-2-2-2002i−2i2i2i2i−2i−2i−2i000000000000000000000
χ14222-22i−2i2-1-1-1-2111002i−2i−i−i−iiii00−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ2300ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ1300000
χ15222-22i−2i2-1-1-1-2111002i−2i−i−i−iiii00ζ7−ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ2300−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ1300000
χ16222-2−2i2i2222-2-2-2-200−2i2i−2i−2i−2i2i2i2i000000000000000000000
χ17222-2−2i2i2-1-1-1-211100−2i2iiii−i−i−i00ζ5−ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ5+ζ1300−ζ7+ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ7−ζ2300000
χ18222-2−2i2i2-1-1-1-211100−2i2iiii−i−i−i00−ζ5+ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ5−ζ1300ζ7−ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ7+ζ2300000
χ192-12222-12-1-1-12-1-122-1-12-1-12-1-1-1-12-1-12-1-1-1-12-1-12-1-100000
χ202-12222-12-1-1-12-1-1-2-2-1-12-1-12-1-111-211-21111-211-21100000
χ212-12222-1-12-1-1-12-122-1-1-12-1-12-1-1-1-12-1-12-1-1-1-12-1-12-100000
χ222-12222-1-12-1-1-12-1-2-2-1-1-12-1-12-1111-211-21111-211-2100000
χ232-12222-1-1-12-1-1-1222-1-1-1-12-1-12-1-1-1-12-1-12-1-1-1-12-1-1200000
χ242-12222-1-1-12-1-1-12-2-2-1-1-1-12-1-121111-211-21111-211-200000
χ252-122-2-2-12-1-1-12-1-12i−2i11-211-211−i−i2i−i−i2i−i−iii−2iii−2iii00000
χ262-122-2-2-12-1-1-12-1-1−2i2i11-211-211ii−2iii−2iii−i−i2i−i−i2i−i−i00000
χ272-122-2-2-1-12-1-1-12-12i−2i111-211-21−i−i−i2i−i−i2i−iiii−2iii−2ii00000
χ282-122-2-2-1-12-1-1-12-1−2i2i111-211-21iii−2iii−2ii−i−i−i2i−i−i2i−i00000
χ292-122-2-2-1-1-12-1-1-122i−2i1111-211-2−i−i−i−i2i−i−i2iiiii−2iii−2i00000
χ302-122-2-2-1-1-12-1-1-12−2i2i1111-211-2iiii−2iii−2i−i−i−i−i2i−i−i2i00000
χ312-12-22i−2i-12-1-11-21100−ii2i−i−i−2iii−ζ7+ζ23ζ7−ζ230−ζ7+ζ23ζ7−ζ230ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130ζ5−ζ13−ζ5+ζ130−ζ5+ζ13ζ5−ζ1300000
χ322-12-22i−2i-12-1-11-21100−ii2i−i−i−2iiiζ7−ζ23−ζ7+ζ230ζ7−ζ23−ζ7+ζ230−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130−ζ5+ζ13ζ5−ζ130ζ5−ζ13−ζ5+ζ1300000
χ332-12-22i−2i-1-12-111-2100−ii−i2i−ii−2ii−ζ7+ζ23ζ7−ζ23ζ7−ζ230−ζ7+ζ23−ζ7+ζ230ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ130ζ5−ζ13ζ5−ζ130−ζ5+ζ1300000
χ342-12-22i−2i-1-12-111-2100−ii−i2i−ii−2iiζ7−ζ23−ζ7+ζ23−ζ7+ζ230ζ7−ζ23ζ7−ζ230−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ130−ζ5+ζ13−ζ5+ζ130ζ5−ζ1300000
χ352-12-22i−2i-1-1-12111-200−ii−i−i2iii−2i−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230ζ7−ζ23−ζ7+ζ230ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130−ζ5+ζ13ζ5−ζ13000000
χ362-12-22i−2i-1-1-12111-200−ii−i−i2iii−2iζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230−ζ7+ζ23ζ7−ζ230−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130ζ5−ζ13−ζ5+ζ13000000
χ372-12-2−2i2i-12-1-11-21100i−i−2iii2i−i−iζ5−ζ13−ζ5+ζ130ζ5−ζ13−ζ5+ζ130−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230−ζ7+ζ23ζ7−ζ230ζ7−ζ23−ζ7+ζ2300000
χ382-12-2−2i2i-12-1-11-21100i−i−2iii2i−i−i−ζ5+ζ13ζ5−ζ130−ζ5+ζ13ζ5−ζ130ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230ζ7−ζ23−ζ7+ζ230−ζ7+ζ23ζ7−ζ2300000
χ392-12-2−2i2i-1-12-111-2100i−ii−2ii−i2i−iζ5−ζ13−ζ5+ζ13−ζ5+ζ130ζ5−ζ13ζ5−ζ130−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ230−ζ7+ζ23−ζ7+ζ230ζ7−ζ2300000
χ402-12-2−2i2i-1-12-111-2100i−ii−2ii−i2i−i−ζ5+ζ13ζ5−ζ13ζ5−ζ130−ζ5+ζ13−ζ5+ζ130ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ230ζ7−ζ23ζ7−ζ230−ζ7+ζ2300000
χ412-12-2−2i2i-1-1-12111-200i−iii−2i−i−i2iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130−ζ5+ζ13ζ5−ζ130−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230ζ7−ζ23−ζ7+ζ23000000
χ422-12-2−2i2i-1-1-12111-200i−iii−2i−i−i2i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130ζ5−ζ13−ζ5+ζ130ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230−ζ7+ζ23ζ7−ζ23000000
χ432424-1000-10000000000000000000000000000000004-1000
χ442424-1000-1000000000000000000000000000000000-41000
χ4548-24-2000100000000000000000000000000000000000000

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