Finite Group Databasebeta

← Group #10690800

Character table — Group #10690800

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order12222222344444444666666612121212121212122244444444666612121212121212121212121212121212121212128888888824242424242424242424242424242424888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ611111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ711111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1
χ811111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-11
χ9111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-1
χ10111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111
χ11111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111
χ12111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-1
χ13111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-11-1
χ14111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-11-11
χ15111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-11-11
χ16111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-11-1
χ1722222222222-2-2-2-2222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ1822222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-222222222-2-2-2-22222000000000000000000000000000000000000
χ19222222222-2-22222-2-222222222222222222-2-222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ20222222222-2-22222-2-2222222222222222-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-1-1-1-1-11111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-1-1-1-1-1111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1111111112222-2-2-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−3000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1111111112222-2-2-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−333000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-222-2-22211111111-1-1-1-1-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−333000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-222-2-22211111111-1-1-1-1-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−3000000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-1-1-1-11111111111111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-1-1-1-11111111111111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000
χ3122222222-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-222111111111111-1-1-1-1-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000
χ3222222222-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-222111111111111-1-1-1-1-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-22222-1-1-1-1-1-1-1-11111-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-22222-1-1-1-1-1-1-1-11111-1-1-1-111111111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-2222222-2-21111-1-1-1-111111111-1-1-1-1-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-2222222-2-21111-1-1-1-111111111-1-1-1-1-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000
χ3722-22-22-2-222i−2i00002i−2i22-2-22-2-2000000002-22i−2i00000022-2-200002i2i−2i−2i00002i2i−2i−2i00001+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3822-22-22-2-222i−2i00002i−2i22-2-22-2-2000000002-22i−2i00000022-2-200002i2i−2i−2i00002i2i−2i−2i0000−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3922-22-22-2-222i−2i00002i−2i22-2-22-2-200000000-22−2i2i000000-2-22200002i2i−2i−2i0000−2i−2i2i2i00001+i−1−i1−i−1+i−1−i1+i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ4022-22-22-2-222i−2i00002i−2i22-2-22-2-200000000-22−2i2i000000-2-22200002i2i−2i−2i0000−2i−2i2i2i0000−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ4122-22-22-2-22−2i2i0000−2i2i22-2-22-2-2000000002-2−2i2i00000022-2-20000−2i−2i2i2i0000−2i−2i2i2i00001−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4222-22-22-2-22−2i2i0000−2i2i22-2-22-2-2000000002-2−2i2i00000022-2-20000−2i−2i2i2i0000−2i−2i2i2i0000−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4322-22-22-2-22−2i2i0000−2i2i22-2-22-2-200000000-222i−2i000000-2-2220000−2i−2i2i2i00002i2i−2i−2i00001−i−1+i1+i−1−i−1+i1−i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ4422-22-22-2-22−2i2i0000−2i2i22-2-22-2-200000000-222i−2i000000-2-2220000−2i−2i2i2i00002i2i−2i−2i0000−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ4522-22-22-2-2-12i−2i00002i−2i-1-111-111−i3−i3−i3−i3i3i3i3i32-22i−2i000000-1-11133−3−3−i−iii33−3−3−i−iii−i3−i3i3i31+i−1−i1−i−1+i1+i−1−i1−i−1+i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000000000
χ4622-22-22-2-2-12i−2i00002i−2i-1-111-111−i3−i3−i3−i3i3i3i3i32-22i−2i000000-1-11133−3−3−i−iii33−3−3−i−iii−i3−i3i3i3−1−i1+i−1+i1−i−1−i1+i−1+i1−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000000000
χ4722-22-22-2-2-12i−2i00002i−2i-1-111-111−i3−i3−i3−i3i3i3i3i3-22−2i2i00000011-1-133−3−3−i−iii−3−333ii−i−ii3i3−i3−i31+i−1−i1−i−1+i−1−i1+i−1+i1−i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000000000
χ4822-22-22-2-2-12i−2i00002i−2i-1-111-111−i3−i3−i3−i3i3i3i3i3-22−2i2i00000011-1-133−3−3−i−iii−3−333ii−i−ii3i3−i3−i3−1−i1+i−1+i1−i1+i−1−i1−i−1+iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000000000
χ4922-22-22-2-2-12i−2i00002i−2i-1-111-111i3i3i3i3−i3−i3−i3−i32-22i−2i000000-1-111−3−333−i−iii−3−333−i−iiii3i3−i3−i31+i−1−i1−i−1+i1+i−1−i1−i−1+i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000000000
χ5022-22-22-2-2-12i−2i00002i−2i-1-111-111i3i3i3i3−i3−i3−i3−i32-22i−2i000000-1-111−3−333−i−iii−3−333−i−iiii3i3−i3−i3−1−i1+i−1+i1−i−1−i1+i−1+i1−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000000000
χ5122-22-22-2-2-12i−2i00002i−2i-1-111-111i3i3i3i3−i3−i3−i3−i3-22−2i2i00000011-1-1−3−333−i−iii33−3−3ii−i−i−i3−i3i3i31+i−1−i1−i−1+i−1−i1+i−1+i1−i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000000000
χ5222-22-22-2-2-12i−2i00002i−2i-1-111-111i3i3i3i3−i3−i3−i3−i3-22−2i2i00000011-1-1−3−333−i−iii33−3−3ii−i−i−i3−i3i3i3−1−i1+i−1+i1−i1+i−1−i1−i−1+iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000000000
χ5322-22-22-2-2-1−2i2i0000−2i2i-1-111-111−i3−i3−i3−i3i3i3i3i32-2−2i2i000000-1-111−3−333ii−i−i−3−333ii−i−i−i3−i3i3i31−i−1+i1+i−1−i1−i−1+i1+i−1−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000000000
χ5422-22-22-2-2-1−2i2i0000−2i2i-1-111-111−i3−i3−i3−i3i3i3i3i32-2−2i2i000000-1-111−3−333ii−i−i−3−333ii−i−i−i3−i3i3i3−1+i1−i−1−i1+i−1+i1−i−1−i1+iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000000000
χ5522-22-22-2-2-1−2i2i0000−2i2i-1-111-111−i3−i3−i3−i3i3i3i3i3-222i−2i00000011-1-1−3−333ii−i−i33−3−3−i−iiii3i3−i3−i31−i−1+i1+i−1−i−1+i1−i−1−i1+i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000000000
χ5622-22-22-2-2-1−2i2i0000−2i2i-1-111-111−i3−i3−i3−i3i3i3i3i3-222i−2i00000011-1-1−3−333ii−i−i33−3−3−i−iiii3i3−i3−i3−1+i1−i−1−i1+i1−i−1+i1+i−1−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.