Finite Group Databasebeta

← Group #10846225

Character table — Group #10846225

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222444444444444444466888888888888888881212121212161616161616161616162424242424242424244848
order1222223444466666888888121212122424242444222466888121224242424242444488466812122424242424448888828
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-11111-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-1
χ3111111111111111111111111111111-1-111111111111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111
χ511111111111111111111-1-11111-1-1-1-111-111-1-1-1-111-1-11111-1-1111-1-1-111-1-1-111-1-1-1-1111111-1-1-1
χ611111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-11-1-1111-1-111-1-1-1-111-1-1-111
χ711111111111111111111-1-11111-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-111-111-1-1-111-1-111-1-1-1-1-1-1111
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111-1-1111-1-1111111-1-1111-1-1
χ91111111111111111-1-1-1-1111111111111-111-1-1-11-1-1-1-1-1-1-1-11111111111-111-1-1-1-1-1-111-1-1-1-111-1
χ101111111111111111-1-1-1-1111111111111-1-1-1-1-1-1111-1-1-1-1-1-11111111-1-1-11-1-11111-1-1-1-1-1-1111-11
χ111111111111111111-1-1-1-11111111111-1-1-111-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1111-111-1-1-1-111-1-11111-1-11
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-11111111111-1-1-11-1
χ131111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1-1111-1-1-1111-1-1-1-1111111-1-1-1-1-1-11
χ141111111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1111-11111-1-1-1-1-1-1111-1-11-1-1-11111-1-111-1-1-1-111-11-1
χ151111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1-111-1111-1-1-1-111-1-1-1-1111111-1
χ161111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111-11111-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-11111-1-11-11
χ172222222-2-2-2-2222222i2i−2i−2i00-2-2-2-2000022000000000002i2i−2i−2i00-2-2200000000000000002i−2i00000
χ182222222-2-2-2-2222222i2i−2i−2i00-2-2-2-20000-2-2000000000002i2i−2i−2i0022-20000000000000000−2i2i00000
χ192222222-2-2-2-222222−2i−2i2i2i00-2-2-2-200002200000000000−2i−2i2i2i00-2-220000000000000000−2i2i00000
χ202222222-2-2-2-222222−2i−2i2i2i00-2-2-2-20000-2-200000000000−2i−2i2i2i0022-200000000000000002i−2i00000
χ21222222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1002222-1-1222-1-1-1-1-1-1-1-1000002-1-12-1-1-1-1-1-100000000000
χ22222222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1002-2-22-1-12-2-2-1-1-1-1-1-1-1-100000-211-211111100000000000
χ23222222-12222-1-1-1-1-12222-2-2-1-1-1-1111100-222-211-22211-1-1-1-11100000-2-1-1-211-1-11100000000000
χ24222222-12222-1-1-1-1-12222-2-2-1-1-1-1111100-2-2-2-211-2-2-211-1-1-1-111000002112-1-111-1-100000000000
χ25222222-12222-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-100-222-2112-2-2111111-1-1000002-1-1-2-1-1111100000000000
χ26222222-12222-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-100-2-2-2-211222111111-1-100000-211211-1-1-1-100000000000
χ27222222-12222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111002222-1-1-2-2-2-1-111111100000-2-1-121111-1-100000000000
χ28222222-12222-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111002-2-22-1-1-222-1-111111100000211-2-1-1-1-11100000000000
χ292222-2-222-22-2222-2-20000222-22-2222222000000-200000000-2-22-2-222000000000000000000-200
χ302222-2-222-22-2222-2-20000222-22-22222-2-2000000-200000000-2-2-222-2-2000000000000000000200
χ312222-2-222-22-2222-2-20000-2-22-22-2-2-2-2-222000000200000000222-2-2-2-2000000000000000000200
χ322222-2-222-22-2222-2-20000-2-22-22-2-2-2-2-2-2-200000020000000022-22222000000000000000000-200
χ332222-2-22-22-22222-2-2000000-22-22000022200-222000-2-2000000-22-2000000000000-22000000000
χ342222-2-22-22-22222-2-2000000-22-22000022-2002-2-200022000000-22-20000000000002-2000000000
χ352222-2-22-22-22222-2-2000000-22-220000-2-2200-222000-2-20000002-220000000000002-2000000000
χ362222-2-22-22-22222-2-2000000-22-220000-2-2-2002-2-2000220000002-22000000000000-22000000000
χ372-22-22-2222-2-2-2-222-22i−2i2i−2i0022-2-2000000000000000002i−2i2i−2i00000000000000000002i−2i002-2000
χ382-22-22-2222-2-2-2-222-22i−2i2i−2i0022-2-2000000000000000002i−2i2i−2i0000000000000000000−2i2i00-22000
χ392-22-22-2222-2-2-2-222-2−2i2i−2i2i0022-2-200000000000000000−2i2i−2i2i00000000000000000002i−2i00-22000
χ402-22-22-2222-2-2-2-222-2−2i2i−2i2i0022-2-200000000000000000−2i2i−2i2i0000000000000000000−2i2i002-2000
χ412-22-22-22-2-222-2-222-22-2-2200-2-22200000002-200002-2002-2-22000000002-20002-20000000000000
χ422-22-22-22-2-222-2-222-22-2-2200-2-2220000000-220000-22002-2-2200000000-22000-220000000000000
χ432-22-22-22-2-222-2-222-2-222-200-2-22200000002-20000-2200-222-2000000002-2000-220000000000000
χ442-22-22-22-2-222-2-222-2-222-200-2-2220000000-2200002-200-222-200000000-220002-20000000000000
χ452-22-22-2-1-2-22211-1-112-2-220011-1-1−i3−i3i3i30002-20−i3i302-2−i3i3-111-1−i3i3000000-110−i3i3-11−i3i300000000000
χ462-22-22-2-1-2-22211-1-112-2-220011-1-1−i3−i3i3i3000-220−i3i30-22−i3i3-111-1−i3i30000001-10i3−i31-1i3−i300000000000
χ472-22-22-2-1-2-22211-1-112-2-220011-1-1i3i3−i3−i30002-20i3−i302-2i3−i3-111-1i3−i3000000-110i3−i3-11i3−i300000000000
χ482-22-22-2-1-2-22211-1-112-2-220011-1-1i3i3−i3−i3000-220i3−i30-22i3−i3-111-1i3−i30000001-10−i3i31-1−i3i300000000000
χ492-22-22-2-1-2-22211-1-11-222-20011-1-1−i3−i3i3i30002-20i3−i30-22i3−i31-1-11−i3i3000000-110−i3i31-1i3−i300000000000
χ502-22-22-2-1-2-22211-1-11-222-20011-1-1−i3−i3i3i3000-220i3−i302-2i3−i31-1-11−i3i30000001-10i3−i3-11−i3i300000000000
χ512-22-22-2-1-2-22211-1-11-222-20011-1-1i3i3−i3−i30002-20−i3i30-22−i3i31-1-11i3−i3000000-110i3−i31-1−i3i300000000000
χ522-22-22-2-1-2-22211-1-11-222-20011-1-1i3i3−i3−i3000-220−i3i302-2−i3i31-1-11i3−i30000001-10−i3i3-11i3−i300000000000
χ53444444-2-4-4-4-4-2-2-2-2-24i4i−4i−4i00222200000000000000000−2i−2i2i2i0000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-2-2−4i−4i4i4i002222000000000000000002i2i−2i−2i0000000000000000000000000000
χ554444-4-4-24-44-4-2-2-222000044-22-22-2-2-2-200000000-4000000002200000000000000000000000000
χ564444-4-4-24-44-4-2-2-2220000-4-4-22-22222200000000400000000-2-200000000000000000000000000
χ574444-4-4-2-44-44-2-2-2220000002-22-2000000400-4-2-20002200000000000000000000000000000000
χ584444-4-4-2-44-44-2-2-2220000002-22-2000000-400422000-2-200000000000000000000000000000000
χ5944-4-400400004-4-4000000−2i22i20000−2i22i2−2i22i24i−4i0000000000000000000022−22000000000000000000000
χ6044-4-400400004-4-4000000−2i22i20000−2i22i2−2i22i2−4i4i00000000000000000000−2222000000000000000000000
χ6144-4-400400004-4-40000002i2−2i200002i2−2i22i2−2i24i−4i00000000000000000000−2222000000000000000000000
χ6244-4-400400004-4-40000002i2−2i200002i2−2i22i2−2i2−4i4i0000000000000000000022−22000000000000000000000
χ634-44-44-4-244-4-422-2-224i−4i4i−4i00-2-22200000000000000000−2i2i−2i2i0000000000000000000000000000
χ644-44-44-4-244-4-422-2-22−4i4i−4i4i00-2-222000000000000000002i−2i2i−2i0000000000000000000000000000
χ654-44-4-4444-4-44-4-44-440000004-4-440000000000000000000000000000000000000000000000000
χ664-44-4-444-444-4-4-44-44000000-444-40000000000000000000000000000000000000000000000000
χ674-44-4-44-24-4-4422-22-2000000-222-20000000000−2i32i30002i3−2i300000000000000000000000000000000
χ684-44-4-44-24-4-4422-22-2000000-222-200000000002i3−2i3000−2i32i300000000000000000000000000000000
χ694-44-4-44-2-444-422-22-20000002-2-22−2i3−2i32i32i3000000000000000002i3−2i300000000000000000000000000
χ704-44-4-44-2-444-422-22-20000002-2-222i32i3−2i3−2i300000000000000000−2i32i300000000000000000000000000
χ7188-8-800-40000-444000000−4i24i200002i2−2i22i2−2i2000000000000000000000000000000000000000000000
χ7288-8-800-40000-4440000004i2−4i20000−2i22i2−2i22i2000000000000000000000000000000000000000000000
χ738-8-880080000-88-80000000000000000000000000000000000000000000000000000000000000
χ748-8-8800-400004-4400000000000026−26−2626000000000000000000000000000000000000000000000
χ758-8-8800-400004-44000000000000−262626−26000000000000000000000000000000000000000000000

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