Finite Group Databasebeta

← Group #10690004

Character table — Group #10690004

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order1222222234444444466666662222444444666666661212121212121212121212121212121244444444121212121212121212121212121212121212888888888888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ91-1-11-11-11111-11-1-1-11-1-111-11-111-1-11ii−i−i-11111-1-1-1-111-1-111-1-1iiii−i−i−i−ii−i1-1ii−i−i1-1ii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ101-1-11-11-11111-11-1-1-11-1-111-11-111-1-11ii−i−i-11111-1-1-1-111-1-111-1-1iiii−i−i−i−ii−i1-1ii−i−i1-1ii−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111-11
χ111-1-11-11-11111-11-1-1-11-1-111-11-111-1-11−i−iii-11111-1-1-1-111-1-111-1-1−i−i−i−iiiii−ii1-1−i−iii1-1−i−iii11-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111-11
χ121-1-11-11-11111-11-1-1-11-1-111-11-111-1-11−i−iii-11111-1-1-1-111-1-111-1-1−i−i−i−iiiii−ii1-1−i−iii1-1−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-11-1
χ131-1-11-11-11111-11-1-1-11-1-111-11-1-1-1111ii−i−i-1-1-1-1-1111111-1-111-1-1iiii−i−i−i−ii−i-11−i−iii1-1ii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1-11
χ141-1-11-11-11111-11-1-1-11-1-111-11-1-1-1111ii−i−i-1-1-1-1-1111111-1-111-1-1iiii−i−i−i−ii−i-11−i−iii1-1ii−i−i-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1111-1
χ151-1-11-11-11111-11-1-1-11-1-111-11-1-1-1111−i−iii-1-1-1-1-1111111-1-111-1-1−i−i−i−iiiii−ii-11ii−i−i1-1−i−iii-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1111-1
χ161-1-11-11-11111-11-1-1-11-1-111-11-1-1-1111−i−iii-1-1-1-1-1111111-1-111-1-1−i−i−i−iiiii−ii-11ii−i−i1-1−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11
χ17222222222222-2-2-22-222222220000-22222-200000000-2-2-2-2222222222222-2-2000000-2-2-2-2-2-2000000000000000000000000000000
χ18222222222222-2-2-22-222222220000-2-2-2-2-2-200000000-2-2-2-22222-2-2-2-2-2-2-2-222000000-2-22222000000000000000000000000000000
χ19222222222-2-2-2222-2222222222222-20000-2222222222222-2-2-2-20000000000-2-20000-2-20000-2-2-2-200000000000000000000000000
χ20222222222-2-2-2222-222222222-2-2-2-2-20000-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000220000-2-20000222200000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-22222222000020000200000000-2-2-2-2-2-2-2-20000000000002-22-2220000000022-2-222-2-2000000000000000000
χ22222222222-2-2-2-2-2-2-2-22222222000020000200000000-2-2-2-2-2-2-2-2000000000000-22-222200000000-2-222-2-222000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122222-2-2-2-22-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2-2-2-1-11111-1-1-1-111111111000000000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-2-2-2-222222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-2-2-2-22-2-2-2-2211111111-1-1-1-1-1-1-1-111111111-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000000000
χ2722222222-1222-2-2-22-2-1-1-1-1-1-1-10000-22222-2−i3−i3i3i3−i3−i3i3i31111-1-1-1-1-1-1-1-1-1-1-1-1-2-2000000111111−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000000
χ2822222222-1222-2-2-22-2-1-1-1-1-1-1-10000-22222-2i3i3−i3−i3i3i3−i3−i31111-1-1-1-1-1-1-1-1-1-1-1-1-2-2000000111111i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000000
χ2922222222-1222-2-2-22-2-1-1-1-1-1-1-10000-2-2-2-2-2-2−i3−i3i3i3−i3−i3i3i31111-1-1-1-1111111112200000011-1-1-1-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3000000000000000000
χ3022222222-1222-2-2-22-2-1-1-1-1-1-1-10000-2-2-2-2-2-2i3i3−i3−i3i3i3−i3−i31111-1-1-1-1111111112200000011-1-1-1-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3000000000000000000
χ3122222222-1-2-2-2222-22-1-1-1-1-1-1-12222-20000-2-1-1-1-1-1-1-1-1-1-1-1-11111−i3−i3i3i3−i3−i3i3i300-2-2000011−i3i3−i3i31111−i3i3i3−i3−i3i3i3−i3000000000000000000
χ3222222222-1-2-2-2222-22-1-1-1-1-1-1-12222-20000-2-1-1-1-1-1-1-1-1-1-1-1-11111i3i3−i3−i3i3i3−i3−i300-2-2000011i3−i3i3−i31111i3−i3−i3i3i3−i3−i3i3000000000000000000
χ3322222222-1-2-2-2222-22-1-1-1-1-1-1-1-2-2-2-2-20000-211111111-1-1-1-11111−i3−i3i3i3−i3−i3i3i30022000011−i3i3−i3i3-1-1-1-1i3−i3−i3i3i3−i3−i3i3000000000000000000
χ3422222222-1-2-2-2222-22-1-1-1-1-1-1-1-2-2-2-2-20000-211111111-1-1-1-11111i3i3−i3−i3i3i3−i3−i30022000011i3−i3i3−i3-1-1-1-1−i3i3i3−i3−i3i3i3−i3000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-10000200002−i3−i3i3i3−i3−i3i3i311111111−i3−i3i3i3−i3−i3i3i300002-22-2-1-1i3−i3i3−i3i3−i3i3−i3-1-111-1-111000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-10000200002−i3−i3i3i3−i3−i3i3i311111111i3i3−i3−i3i3i3−i3−i30000-22-22-1-1−i3i3−i3i3i3−i3i3−i311-1-111-1-1000000000000000000
χ3722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-10000200002i3i3−i3−i3i3i3−i3−i311111111−i3−i3i3i3−i3−i3i3i30000-22-22-1-1i3−i3i3−i3−i3i3−i3i311-1-111-1-1000000000000000000
χ3822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-10000200002i3i3−i3−i3i3i3−i3−i311111111i3i3−i3−i3i3i3−i3−i300002-22-2-1-1−i3i3−i3i3−i3i3−i3i3-1-111-1-111000000000000000000
χ39222-2-2-2-222000-22-202222-2-2-2-22-22-20000002-22-22-22-22-22-200000000000000000000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2000000
χ40222-2-2-2-222000-22-202222-2-2-2-22-22-20000002-22-22-22-22-22-200000000000000000000000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2000000
χ41222-2-2-2-222000-22-202222-2-2-2-2-22-22000000-22-22-22-222-22-200000000000000000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2000000
χ42222-2-2-2-222000-22-202222-2-2-2-2-22-22000000-22-22-22-222-22-200000000000000000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2000000
χ4322-2-222-2-222-2-2000202-2-2-222-2000002i−2i2i−2i00000000000002-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000002−22−22−22−20000−i2i2−i2i200
χ4422-2-222-2-222-2-2000202-2-2-222-2000002i−2i2i−2i00000000000002-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000−22−22−22−220000i2−i2i2−i200
χ4522-2-222-2-222-2-2000202-2-2-222-200000−2i2i−2i2i00000000000002-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000002−22−22−22−20000i2−i2i2−i200
χ4622-2-222-2-222-2-2000202-2-2-222-200000−2i2i−2i2i00000000000002-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000−22−22−22−220000−i2i2−i2i200
χ472-22-2-222-222-22000-20-22-2-2-222000002-2-2200000000000002-2-222-22-2-22-2200000000000000000000000000−i2i2−i2i2i2−i2i2−i20000−i2i2i2−i200
χ482-22-2-222-222-22000-20-22-2-2-222000002-2-2200000000000002-2-222-22-2-22-2200000000000000000000000000i2−i2i2−i2−i2i2−i2i20000i2−i2−i2i200
χ492-22-2-222-222-22000-20-22-2-2-22200000-222-200000000000002-2-22-22-222-22-200000000000000000000000000−i2i2−i2i2i2−i2i2−i20000i2−i2−i2i200
χ502-22-2-222-222-22000-20-22-2-2-22200000-222-200000000000002-2-22-22-222-22-200000000000000000000000000i2−i2i2−i2−i2i2−i2i20000−i2i2i2−i200
χ512-2-22-22-22222-2-222-2-2-2-222-22-20000-22i2i−2i−2i200000000-2-22222-2-22i2i2i2i−2i−2i−2i−2i−2i2i000000-22−2i−2i2i2i000000000000000000000000000000
χ522-2-22-22-22222-2-222-2-2-2-222-22-20000-2−2i−2i2i2i200000000-2-22222-2-2−2i−2i−2i−2i2i2i2i2i2i−2i000000-222i2i−2i−2i000000000000000000000000000000
χ532-2-22-22-222-2-222-2-222-2-222-22-222-2-2-2000022222-2-2-2-222-2-2-2-2220000000000-220000-220000-2-22200000000000000000000000000
χ542-2-22-22-222-2-222-2-222-2-222-22-2-2-222-200002-2-2-2-2222222-2-2-2-22200000000002-20000-22000022-2-200000000000000000000000000
χ552-2-22-22-222-2-22-2222-2-2-222-22-2000020000-200000000-2-222-2-2220000000000002i−2i−2i2i2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ562-2-22-22-222-2-22-2222-2-2-222-22-2000020000-200000000-2-222-2-222000000000000−2i2i2i−2i2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ572-2-22-22-22-122-22-2-2-2211-1-11-1122-2-222i2i−2i−2i-2-1-1-1-11111-1-111-1-111−i−i−i−iiiii2i−2i2-22i2i−2i−2i-11−i−iii-1-111−i−i−i−iiiii000000000000000000
χ582-2-22-22-22-122-22-2-2-2211-1-11-1122-2-22−2i−2i2i2i-2-1-1-1-11111-1-111-1-111iiii−i−i−i−i−2i2i2-2−2i−2i2i2i-11ii−i−i-1-111iiii−i−i−i−i000000000000000000
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χ602-2-22-22-22-122-22-2-2-2211-1-11-11-2-2222−2i−2i2i2i-21111-1-1-1-1-1-111-1-111iiii−i−i−i−i−2i2i-222i2i−2i−2i-11ii−i−i11-1-1−i−i−i−iiiii000000000000000000
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χ632-2-22-22-22-122-2-222-2-211-1-11-110000-2−2i−2i2i2i2−i3−i3i3i3i3i3−i3−i311-1-1-1-111iiii−i−i−i−i2i−2i0000001-1−i−iii−i3i3i3−i3−33−333−33−3000000000000000000
χ642-2-22-22-22-122-2-222-2-211-1-11-110000-2−2i−2i2i2i2i3i3−i3−i3−i3−i3i3i311-1-1-1-111iiii−i−i−i−i2i−2i0000001-1−i−iiii3−i3−i3i33−33−3−33−33000000000000000000
χ652-2-22-22-22-1-2-222-2-22211-1-11-1122-2-2-200002-1-1-1-11111-1-11111-1-133−3−3−3−33300-2200001-13−3−3311-1-13−3−33−333−3000000000000000000
χ662-2-22-22-22-1-2-222-2-22211-1-11-1122-2-2-200002-1-1-1-11111-1-11111-1-1−3−33333−3−300-2200001-1−333−311-1-1−333−33−3−33000000000000000000
χ672-2-22-22-22-1-2-222-2-22211-1-11-11-2-222-2000021111-1-1-1-1-1-11111-1-133−3−3−3−333002-200001-13−3−33-1-111−333−33−3−33000000000000000000
χ682-2-22-22-22-1-2-222-2-22211-1-11-11-2-222-2000021111-1-1-1-1-1-11111-1-1−3−33333−3−3002-200001-1−333−3-1-1113−3−33−333−3000000000000000000
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χ702-2-22-22-22-1-2-22-2222-211-1-11-11000020000-2−i3−i3i3i3i3i3−i3−i311-1-111-1-1−3−33333−3−30000−2i2i2i−2i-113−3−33i3−i3−i3i3ii−i−i−i−iii000000000000000000
χ712-2-22-22-22-1-2-22-2222-211-1-11-11000020000-2i3i3−i3−i3−i3−i3i3i311-1-111-1-133−3−3−3−3330000−2i2i2i−2i-11−333−3−i3i3i3−i3ii−i−i−i−iii000000000000000000
χ722-2-22-22-22-1-2-22-2222-211-1-11-11000020000-2i3i3−i3−i3−i3−i3i3i311-1-111-1-1−3−33333−3−300002i−2i−2i2i-113−3−33−i3i3i3−i3−i−iiiii−i−i000000000000000000
χ732-2-2-22-2222000-2-2202-2-22-22-222-2-220000002-22-2-22-222-2-220000000000000000000000000000000000000022−2−2−2−2222−2−22000000
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χ894-4444-4-4-4400000000-44-444-4-40000000000000000000000000000000000000000000000000000000000002-2-22-222-20000000000
χ904-4444-4-4-4400000000-44-444-4-4000000000000000000000000000000000000000000000000000000000000-222-22-2-220000000000
χ914-44-4-444-44-44-400040-44-4-4-4440000000000000000000000-444-40000000000000000000000000000000000000000000000000000
χ924-44-4-444-4-24-44000-402-2222-2-2000004-4-440000000000000-222-2-22-222-22-200000000000000000000000000000000000000000000
χ934-44-4-444-4-24-44000-402-2222-2-200000-444-40000000000000-222-22-22-2-22-2200000000000000000000000000000000000000000000
χ944-44-4-444-4-2-44-4000402-2222-2-200000000000000000000002-2-22−2i32i32i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000
χ954-44-4-444-4-2-44-4000402-2222-2-200000000000000000000002-2-222i3−2i3−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000
χ964-4-4-44-444400044-40-4-4-44-44-44000000000000000000-444-400000000000000000000000000000000000000000000000000000000
χ974-4-4-44-444-200044-40-422-22-22-20000000000−2i32i32i3−2i32i3−2i3−2i32i32-2-2200000000000000000000000000000000000000000000000000000000
χ984-4-4-44-444-200044-40-422-22-22-200000000002i3−2i3−2i32i3−2i32i32i3−2i32-2-2200000000000000000000000000000000000000000000000000000000
χ994-4-4-44-444-2000-4-440422-22-22-24-4-44000000-22-222-22-2-222-200000000000000000000000000000000000000000000000000000000
χ1004-4-4-44-444-2000-4-440422-22-22-2-444-40000002-22-2-22-22-222-200000000000000000000000000000000000000000000000000000000
χ10188-88-8-88-8-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8888-8-8-8-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).