Finite Group Databasebeta

← Group #10877287

Character table — Group #10877287

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12222222222234444444466666661212121212121212444444446666121212121212121212121212121212121212121288888888242424242424242424242424242424244444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111-1-1-1-11111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ61111111111111-1-1-1-11111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ71111111111111-1-1-1-11111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111-1-1-1-11111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1011111111-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1111111111-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ1211111111-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-111-1-1
χ1311111111-1-1-1-11-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ1411111111-1-1-1-11-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1
χ1511111111-1-1-1-11-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-1
χ1611111111-1-1-1-11-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111
χ1722222222222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ21222222222222-12222-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−30000000000000000
χ22222222222222-12222-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−3330000000000000000
χ23222222222222-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ24222222222222-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−3330000000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−30000000000000000
χ2722222222-2-2-2-222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2822222222-2-2-2-22-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2922222222-2-2-2-2-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-211111111-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ3022222222-2-2-2-2-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-211111111-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ3122222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000033−3−3−3−33333−3−3−3−3330000000000000000
χ3222222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−3−33333−3−3−3−33333−3−30000000000000000
χ3322222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2221111111111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ3422222222-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2221111111111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ3522222222-2-2-2-2-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−30000000000000000
χ3622222222-2-2-2-2-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−3330000000000000000
χ3722-222-2-2-222-2-22000022-2-222-2-22-2-22222-2-2-2-2002-2000022-2-222-2-200000000000000000000000000000000000000002-22-2000000000000
χ3822-222-2-2-222-2-22000022-2-222-2-22-2-22222-2-2-2-2002-2000022-2-222-2-20000000000000000000000000000000000000000-22-22000000000000
χ3922-222-2-2-222-2-220000-2-22222-2-22-2-2-2-2-2-2222200-22000022-2-2-2-222000000000000000000000000000000000000000000002i−2i00002i−2i0000
χ4022-222-2-2-222-2-220000-2-22222-2-22-2-2-2-2-2-2222200-22000022-2-2-2-22200000000000000000000000000000000000000000000−2i2i0000−2i2i0000
χ4122-222-2-2-2-2-2222000022-2-222-2-22-2-22222-2-2-2-200-220000-2-222-2-22200000000000000000000000000000000000000002-2-22000000000000
χ4222-222-2-2-2-2-2222000022-2-222-2-22-2-22222-2-2-2-200-220000-2-222-2-2220000000000000000000000000000000000000000-222-2000000000000
χ4322-222-2-2-2-2-22220000-2-22222-2-22-2-2-2-2-2-22222002-20000-2-22222-2-2000000000000000000000000000000000000000000002i−2i0000−2i2i0000
χ4422-222-2-2-2-2-22220000-2-22222-2-22-2-2-2-2-2-22222002-20000-2-22222-2-200000000000000000000000000000000000000000000−2i2i00002i−2i0000
χ4522-2-2-22-222-22-222i2i−2i−2i00002-22-2-22-2000000002i−2i0000002-22-200002i2i−2i−2i00002i2i−2i−2i00002−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ4622-2-2-22-222-22-222i2i−2i−2i00002-22-2-22-2000000002i−2i0000002-22-200002i2i−2i−2i00002i2i−2i−2i0000−22−22i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ4722-2-2-22-222-22-22−2i−2i2i2i00002-22-2-22-200000000−2i2i0000002-22-20000−2i−2i2i2i0000−2i−2i2i2i00002−22−2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ4822-2-2-22-222-22-22−2i−2i2i2i00002-22-2-22-200000000−2i2i0000002-22-20000−2i−2i2i2i0000−2i−2i2i2i0000−22−22−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ4922-2-2-22-222-22-2-12i2i−2i−2i0000-11-111-1133−3−333−3−32i−2i000000-11-113−33−3−i−iii−i3−i3i3i3−i−iii−i3−i3i3i32−22−2−i2i2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ5022-2-2-22-222-22-2-12i2i−2i−2i0000-11-111-1133−3−333−3−32i−2i000000-11-113−33−3−i−iii−i3−i3i3i3−i−iii−i3−i3i3i3−22−22i2−i2i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ5122-2-2-22-222-22-2-12i2i−2i−2i0000-11-111-11−3−333−3−3332i−2i000000-11-11−33−33−i−iiii3i3−i3−i3−i−iiii3i3−i3−i32−22−2−i2i2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ5222-2-2-22-222-22-2-12i2i−2i−2i0000-11-111-11−3−333−3−3332i−2i000000-11-11−33−33−i−iiii3i3−i3−i3−i−iiii3i3−i3−i3−22−22i2−i2i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ5322-2-2-22-222-22-2-1−2i−2i2i2i0000-11-111-1133−3−333−3−3−2i2i000000-11-113−33−3ii−i−ii3i3−i3−i3ii−i−ii3i3−i3−i32−22−2i2−i2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ5422-2-2-22-222-22-2-1−2i−2i2i2i0000-11-111-1133−3−333−3−3−2i2i000000-11-113−33−3ii−i−ii3i3−i3−i3ii−i−ii3i3−i3−i3−22−22−i2i2−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ5522-2-2-22-222-22-2-1−2i−2i2i2i0000-11-111-11−3−333−3−333−2i2i000000-11-11−33−33ii−i−i−i3−i3i3i3ii−i−i−i3−i3i3i32−22−2i2−i2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ5622-2-2-22-222-22-2-1−2i−2i2i2i0000-11-111-11−3−333−3−333−2i2i000000-11-11−33−33ii−i−i−i3−i3i3i3ii−i−i−i3−i3i3i3−22−22−i2i2−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ5722-2-2-22-22-22-2222i2i−2i−2i00002-22-2-22-200000000−2i2i000000-22-2200002i2i−2i−2i0000−2i−2i2i2i00002−2−22−i2i2i2−i22−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ5822-2-2-22-22-22-2222i2i−2i−2i00002-22-2-22-200000000−2i2i000000-22-2200002i2i−2i−2i0000−2i−2i2i2i0000−222−2i2−i2−i2i2−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ5922-2-2-22-22-22-222−2i−2i2i2i00002-22-2-22-2000000002i−2i000000-22-220000−2i−2i2i2i00002i2i−2i−2i00002−2−22i2−i2−i2i22−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ6022-2-2-22-22-22-222−2i−2i2i2i00002-22-2-22-2000000002i−2i000000-22-220000−2i−2i2i2i00002i2i−2i−2i0000−222−2−i2i2i2−i2−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ6122-2-2-22-22-22-22-12i2i−2i−2i0000-11-111-1133−3−333−3−3−2i2i0000001-11-1−33−33−i−iii−i3−i3i3i3ii−i−ii3i3−i3−i32−2−22−i2i2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000000000000
χ6222-2-2-22-22-22-22-12i2i−2i−2i0000-11-111-1133−3−333−3−3−2i2i0000001-11-1−33−33−i−iii−i3−i3i3i3ii−i−ii3i3−i3−i3−222−2i2−i2−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
χ6322-2-2-22-22-22-22-12i2i−2i−2i0000-11-111-11−3−333−3−333−2i2i0000001-11-13−33−3−i−iiii3i3−i3−i3ii−i−i−i3−i3i3i32−2−22−i2i2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000000000000
χ6422-2-2-22-22-22-22-12i2i−2i−2i0000-11-111-11−3−333−3−333−2i2i0000001-11-13−33−3−i−iiii3i3−i3−i3ii−i−i−i3−i3i3i3−222−2i2−i2−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000000000000
χ6522-2-2-22-22-22-22-1−2i−2i2i2i0000-11-111-1133−3−333−3−32i−2i0000001-11-1−33−33ii−i−ii3i3−i3−i3−i−iii−i3−i3i3i32−2−22i2−i2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000000000000
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χ1084-4-4-44-4440000-20000-444-422-2-2-2222-22-2-22-22000000000000000000000000−232323−23−232323−230000000000000000000000000000000000000000

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