Finite Group Databasebeta

← Group #10696884

Character table — Group #10696884

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order12222234466644444661212121212121212888812122424242424242424444412121212121212128888448888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111
χ9222222222222-2-2-22-222-2-2-2-222-2-200002-20000000000000000000000002-20000
χ10222222222222-2-2-22-222-2-2-2-222-2-200002-2000000000000000000000000-220000
χ112222222-2-222222-2-2-2222222-2-2-2-20000-2-200000000000000000000000000002i−2i
χ122222222-2-222222-2-2-2222222-2-2-2-20000-2-20000000000000000000000000000−2i2i
χ132222222-2-2222-2-22-2222-2-2-2-2-2-22222-2-2-222222-2-2-2-20000000000000000000000
χ142222222-2-2222-2-22-2222-2-2-2-2-2-222-2-222-22-2-2-2-222220000000000000000000000
χ15222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ16222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ17222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-111110000000000
χ18222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-10000000000
χ19222222-1-2-2-1-1-1-2-22-22-1-1111111-1-122-2-21-1-1-1-1-111110000−i3i3−i3i3−i3−i3i3i30000000000
χ20222222-1-2-2-1-1-1-2-22-22-1-1111111-1-122-2-21-1-1-1-1-111110000i3−i3i3−i3i3i3−i3−i30000000000
χ21222222-1-2-2-1-1-1-2-22-22-1-1111111-1-1-2-2221-11111-1-1-1-10000−i3i3−i3i3i3i3−i3−i30000000000
χ22222222-1-2-2-1-1-1-2-22-22-1-1111111-1-1-2-2221-11111-1-1-1-10000i3−i3i3−i3−i3−i3i3i30000000000
χ232222-2-22222222-22-2-2-2-222-2-222220000-2-2000000002-20022-2-200000000000000
χ242222-2-22222222-22-2-2-2-222-2-222220000-2-200000000-2200-2-22200000000000000
χ252222-2-2222222-22-2-22-2-2-2-22222-2-20000-22000000000000000000000000002-200
χ262222-2-2222222-22-2-22-2-2-2-22222-2-20000-2200000000000000000000000000-2200
χ272222-2-22-2-22222-2-222-2-222-2-2-2-2-2-20000220000000000000000000022-2-2000000
χ282222-2-22-2-22222-2-222-2-222-2-2-2-2-2-200002200000000000000000000-2-222000000
χ292222-2-22-2-2222-2222-2-2-2-2-222-2-22200002-200000000002-200002-22-20000000000
χ302222-2-22-2-2222-2222-2-2-2-2-222-2-22200002-20000000000-220000-22-220000000000
χ312222-2-2-122-1-1-12-22-2-211-1-111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i32-200-1-111−i3i3i3−i30000000000
χ322222-2-2-122-1-1-12-22-2-211-1-111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i3-220011-1-1i3−i3−i3i30000000000
χ332222-2-2-122-1-1-12-22-2-211-1-111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i32-200-1-111i3−i3−i3i30000000000
χ342222-2-2-122-1-1-12-22-2-211-1-111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i3-220011-1-1−i3i3i3−i30000000000
χ352222-2-2-1-2-2-1-1-1-2222-21111-1-111-1-10000-11−i3−i3i3i3i3i3−i3−i3002-2−i3i3i3−i3-11-110000000000
χ362222-2-2-1-2-2-1-1-1-2222-21111-1-111-1-10000-11−i3−i3i3i3i3i3−i3−i300-22i3−i3−i3i31-11-10000000000
χ372222-2-2-1-2-2-1-1-1-2222-21111-1-111-1-10000-11i3i3−i3−i3−i3−i3i3i3002-2i3−i3−i3i3-11-110000000000
χ382222-2-2-1-2-2-1-1-1-2222-21111-1-111-1-10000-11i3i3−i3−i3−i3−i3i3i300-22−i3i3i3−i31-11-10000000000
χ39444444-244-2-2-2-4-4-44-4-2-22222-2-2220000-22000000000000000000000000000000
χ40444444-2-4-4-2-2-244-4-4-4-2-2-2-2-2-22222000022000000000000000000000000000000
χ414444-4-4-244-2-2-2-44-4-442222-2-2-2-22200002-2000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-24-4-44422-2-22222220000-2-2000000000000000000000000000000
χ4344-4-40044-4-44-4000000000004-400000000000000000000000000002-22-2000000
χ4444-4-40044-4-44-4000000000004-40000000000000000000000000000-22-22000000
χ4544-4-4004-44-44-400000000000-4400000000000000000000000000002-2-22000000
χ4644-4-4004-44-44-400000000000-440000000000000000000000000000-222-2000000
χ474-44-44-44004-4-4000004-4000000000022−2200000022−2222−220000000000000000000000
χ484-44-44-44004-4-4000004-40000000000−2222000000−2222−22220000000000000000000000
χ494-44-44-4-200-22200000-22−2i32i3−2i32i300000022−2200i6−i6i6−i6−22−220000000000000000000000
χ504-44-44-4-200-22200000-22−2i32i3−2i32i3000000−222200−i6i6−i6i62−22−20000000000000000000000
χ514-44-44-4-200-22200000-222i3−2i32i3−2i300000022−2200−i6i6−i6i6−22−220000000000000000000000
χ524-44-44-4-200-22200000-222i3−2i32i3−2i3000000−222200i6−i6i6−i62−22−20000000000000000000000
χ534-44-4-444004-4-400000-440000000022−22000022−22−222200000000000000000000000000
χ544-44-4-444004-4-400000-4400000000−22220000−222222−2200000000000000000000000000
χ554-44-4-44-200-222000002-2−2i32i32i3−2i3000022−220000−222−2i6−i6−i6i60000000000000000000000
χ564-44-4-44-200-222000002-2−2i32i32i3−2i30000−222200002−2−22−i6i6i6−i60000000000000000000000
χ574-44-4-44-200-222000002-22i3−2i3−2i32i3000022−220000−222−2−i6i6i6−i60000000000000000000000
χ584-44-4-44-200-222000002-22i3−2i3−2i32i30000−222200002−2−22i6−i6−i6i60000000000000000000000
χ5988-8-800-48-84-4400000000000-4400000000000000000000000000000000000000
χ6088-8-800-4-884-44000000000004-400000000000000000000000000000000000000
χ618-8-8800800-8-88000000000000000000000000000000000000000000000000000
χ628-8-8800-40044-40000000000000−4i34i3000000000000000000000000000000000000
χ638-8-8800-40044-400000000000004i3−4i3000000000000000000000000000000000000

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