Finite Group Databasebeta

← Group #10826301

Character table — Group #10826301

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order122222223444444446666666121212121212121222444466668888888812121212242424242424242424242424242424242466888812121212121224242424242424244444222222444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-11-1
χ101111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-11
χ111111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-11
χ121111111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-1
χ131111111111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-11
χ141111111111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111-1
χ151111111111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1111-1
χ161111111111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-11
χ17222222222-22222-2-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000022220000000000000000-2-2-2-2000022-2-222000000000000000000000000
χ18222222222-22222-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000022220000-2-222-2-2000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2222200000000-2-2-2-200000000000000002-222000022-2-2-2-2000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222222200000000-2-2-2-20000000000000000-22-2-20000-2-22222000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111122-1-1-2-2-2-2-1-1-1-1-1-1111111110000000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2-2-2111111111111110000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2112222111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-111111111-221122-2-2-1-1-1-111-1-1-1-111110000000000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-2211-2-222-1-1-1-1111111-1-1-1-10000000000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211112222-2-2-2-21111-1-1-1-1-1-1-1-1111111112-2-1-1-2-2221111-1-11111-1-1-1-10000000000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111-2-2-2-22222111111111111-1-1-1-1-1-1-1-12-2-1-122-2-21111-1-1-1-1-1-111110000000000000000
χ2922222222-1-22222-2-2-2-1-1-1-1-1-1-111111111-2-22222111100000000-1-1-1-13333−3−3−3−33333−3−3−3−3-2-2110000-1-111-1-133−3−333−3−30000000000000000
χ3022222222-1-22222-2-2-2-1-1-1-1-1-1-111111111-2-22222111100000000-1-1-1-1−3−3−3−33333−3−3−3−33333-2-2110000-1-111-1-1−3−333−3−3330000000000000000
χ3122222222-1-22222-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2111100000000-1-1-1-13333−3−3−3−33333−3−3−3−322-1-1000011-1-111−3−333−3−3330000000000000000
χ3222222222-1-22222-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-2111100000000-1-1-1-1−3−3−3−33333−3−3−3−3333322-1-1000011-1-11133−3−333−3−30000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-1-1-1-10000000011113333−3−3−3−3−3−3−3−333332-2-1-10000-1-1111133−3−3−3−3330000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-1-1-1-1000000001111−3−3−3−333333333−3−3−3−32-2-1-10000-1-11111−3−33333−3−30000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-1-1-1-10000000011113333−3−3−3−3−3−3−3−33333-2211000011-1-1-1-1−3−33333−3−30000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-1-1-1-1000000001111−3−3−3−333333333−3−3−3−3-2211000011-1-1-1-133−3−3−3−3330000000000000000
χ3722-222-2-2-2202i2i−2i−2i00022-2-22-2-200000000002-22i−2i0000−i2−i2i2i222−2−22i2i−2i−2i−i2−i2i2i2−i2−i2i2i222−2−222−2−20000−i2i22−22-2002i−2i−i2i2−i2i22−22−20000000000000000
χ3822-222-2-2-2202i2i−2i−2i00022-2-22-2-200000000002-22i−2i0000i2i2−i2−i2−2−2222i2i−2i−2ii2i2−i2−i2i2i2−i2−i2−2−222−2−2220000i2−i2−222-2002i−2ii2−i2i2−i2−22−220000000000000000
χ3922-222-2-2-2202i2i−2i−2i00022-2-22-2-20000000000-22−2i2i0000−i2−i2i2i222−2−22i2i−2i−2i−i2−i2i2i2−i2−i2i2i222−2−222−2−20000i2−i2−22-2200−2i2ii2−i2i2−i2−22−220000000000000000
χ4022-222-2-2-2202i2i−2i−2i00022-2-22-2-20000000000-22−2i2i0000i2i2−i2−i2−2−2222i2i−2i−2ii2i2−i2−i2i2i2−i2−i2−2−222−2−2220000−i2i22−2-2200−2i2i−i2i2−i2i22−22−20000000000000000
χ4122-222-2-2-220−2i−2i2i2i00022-2-22-2-200000000002-2−2i2i0000−i2−i2i2i2−2−222−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000−i2i2−222-200−2i2i−i2i2−i2i2−22−220000000000000000
χ4222-222-2-2-220−2i−2i2i2i00022-2-22-2-200000000002-2−2i2i0000i2i2−i2−i222−2−2−2i−2i2i2ii2i2−i2−i2i2i2−i2−i222−2−222−2−20000i2−i22−22-200−2i2ii2−i2i2−i22−22−20000000000000000
χ4322-222-2-2-220−2i−2i2i2i00022-2-22-2-20000000000-222i−2i0000−i2−i2i2i2−2−222−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000i2−i22−2-22002i−2ii2−i2i2−i22−22−20000000000000000
χ4422-222-2-2-220−2i−2i2i2i00022-2-22-2-20000000000-222i−2i0000i2i2−i2−i222−2−2−2i−2i2i2ii2i2−i2−i2i2i2−i2−i222−2−222−2−20000−i2i2−22-22002i−2i−i2i2−i2i2−22−220000000000000000
χ4522-222-2-2-2-102i2i−2i−2i000-1-111-1113−333−3−33−3002-22i−2i−i3−i3i3i3−i2−i2i2i222−2−2−i−iiiζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700−i3i3−i2i22−2-113−3−iiζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ4622-222-2-2-2-102i2i−2i−2i000-1-111-1113−333−3−33−3002-22i−2i−i3−i3i3i3i2i2−i2−i2−2−222−i−iii−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700−i3i3i2−i2−22-113−3−ii−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ4722-222-2-2-2-102i2i−2i−2i000-1-111-1113−333−3−33−300-22−2i2i−i3−i3i3i3−i2−i2i2i222−2−2−i−iiiζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700i3−i3i2−i2−221-1−33i−i−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ4822-222-2-2-2-102i2i−2i−2i000-1-111-1113−333−3−33−300-22−2i2i−i3−i3i3i3i2i2−i2−i2−2−222−i−iii−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700i3−i3−i2i22−21-1−33i−iζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ4922-222-2-2-2-102i2i−2i−2i000-1-111-111−33−3−333−33002-22i−2ii3i3−i3−i3−i2−i2i2i222−2−2−i−iiiζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300i3−i3−i2i22−2-11−33−iiζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ5022-222-2-2-2-102i2i−2i−2i000-1-111-111−33−3−333−33002-22i−2ii3i3−i3−i3i2i2−i2−i2−2−222−i−iii−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300i3−i3i2−i2−22-11−33−ii−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ5122-222-2-2-2-102i2i−2i−2i000-1-111-111−33−3−333−3300-22−2i2ii3i3−i3−i3−i2−i2i2i222−2−2−i−iiiζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300−i3i3i2−i2−221-13−3i−i−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ5222-222-2-2-2-102i2i−2i−2i000-1-111-111−33−3−333−3300-22−2i2ii3i3−i3−i3i2i2−i2−i2−2−222−i−iii−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300−i3i3−i2i22−21-13−3i−iζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ5322-222-2-2-2-10−2i−2i2i2i000-1-111-1113−333−3−33−3002-2−2i2ii3i3−i3−i3−i2−i2i2i2−2−222ii−i−iζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700i3−i3−i2i2−22-113−3i−iζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ5422-222-2-2-2-10−2i−2i2i2i000-1-111-1113−333−3−33−3002-2−2i2ii3i3−i3−i3i2i2−i2−i222−2−2ii−i−i−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700i3−i3i2−i22−2-113−3i−i−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ5522-222-2-2-2-10−2i−2i2i2i000-1-111-1113−333−3−33−300-222i−2ii3i3−i3−i3−i2−i2i2i2−2−222ii−i−iζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700−i3i3i2−i22−21-1−33−ii−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000000000
χ5622-222-2-2-2-10−2i−2i2i2i000-1-111-1113−333−3−33−300-222i−2ii3i3−i3−i3i2i2−i2−i222−2−2ii−i−i−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700−i3i3−i2i2−221-1−33−iiζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000000000
χ5722-222-2-2-2-10−2i−2i2i2i000-1-111-111−33−3−333−33002-2−2i2i−i3−i3i3i3−i2−i2i2i2−2−222ii−i−iζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300−i3i3−i2i2−22-11−33i−iζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000000000
χ5822-222-2-2-2-10−2i−2i2i2i000-1-111-111−33−3−333−33002-2−2i2i−i3−i3i3i3i2i2−i2−i222−2−2ii−i−i−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300−i3i3i2−i22−2-11−33i−i−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
χ5922-222-2-2-2-10−2i−2i2i2i000-1-111-111−33−3−333−3300-222i−2i−i3−i3i3i3−i2−i2i2i2−2−222ii−i−iζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300i3−i3i2−i22−21-13−3−ii−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.