Finite Group Databasebeta

← Group #10696813

Character table — Group #10696813

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222222222444444444888888888888888816161616161616161616161624242424484848484848
order122222344666666644444121212128888121212122424242424242424222466666612128888448888
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
χ51111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1
χ61111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111
χ81111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1
χ92222222222222222-2-22-2-222220000-2-2-2-200000000002-2000022-2-20000000000
χ102222222222222222-2-22-2-222220000-2-2-2-20000000000-220000-2-2220000000000
χ112222222-2-2222222222-2-2-2-2-2-2-2000022-2-200000000000000000000000000002i−2i
χ122222222-2-2222222222-2-2-2-2-2-2-2000022-2-20000000000000000000000000000−2i2i
χ132222222-2-22222222-2-2-222-2-2-2-20000-2-2220000000000000000000022-2-2000000
χ142222222-2-22222222-2-2-222-2-2-2-20000-2-22200000000000000000000-2-222000000
χ15222222-122-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ16222222-122-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ17222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-111110000000000
χ18222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-10000000000
χ19222222-122-1-1-1-1-1-1-1-2-22-2-2-1-1-1-100001111−i3−i3−i3−i3i3i3i3i3002-2−i3−i3i3i3-1-1110000000000
χ20222222-122-1-1-1-1-1-1-1-2-22-2-2-1-1-1-100001111−i3−i3−i3−i3i3i3i3i300-22i3i3−i3−i311-1-10000000000
χ21222222-122-1-1-1-1-1-1-1-2-22-2-2-1-1-1-100001111i3i3i3i3−i3−i3−i3−i3002-2i3i3−i3−i3-1-1110000000000
χ22222222-122-1-1-1-1-1-1-1-2-22-2-2-1-1-1-100001111i3i3i3i3−i3−i3−i3−i300-22−i3−i3i3i311-1-10000000000
χ232222-2-2222-2-2-2-22222-2-22-222-2-200002-22-20000000000000000000000002-20000
χ242222-2-2222-2-2-2-22222-2-22-222-2-200002-22-2000000000000000000000000-220000
χ252222-2-2222-2-2-2-2222-22-2-2222-2-20000-22-22000000000000000000000000002-200
χ262222-2-2222-2-2-2-2222-22-2-2222-2-20000-22-2200000000000000000000000000-2200
χ272222-2-22-2-2-2-2-2-22222-22-22-2-22222-2-22-2-2222-2-222-2-20000000000000000000000
χ282222-2-22-2-2-2-2-2-22222-22-22-2-222-2-2222-2-22-2-222-2-2220000000000000000000000
χ292222-2-22-2-2-2-2-2-2222-2222-2-2-2220000-222-2000000002-2002-22-200000000000000
χ302222-2-22-2-2-2-2-2-2222-2222-2-2-2220000-222-200000000-2200-22-2200000000000000
χ312222-2-2-1-2-21111-1-1-12-22-2211-1-122-2-2-111-1-1-111-1-1110000−i3i3i3−i3−i3i3−i3i30000000000
χ322222-2-2-1-2-21111-1-1-12-22-2211-1-122-2-2-111-1-1-111-1-1110000i3−i3−i3i3i3−i3i3−i30000000000
χ332222-2-2-1-2-21111-1-1-12-22-2211-1-1-2-222-111-111-1-111-1-10000−i3i3i3−i3i3−i3i3−i30000000000
χ342222-2-2-1-2-21111-1-1-12-22-2211-1-1-2-222-111-111-1-111-1-10000i3−i3−i3i3−i3i3−i3i30000000000
χ352222-2-2-1-2-21111-1-1-1-2222-211-1-100001-1-11−i3−i3i3i3i3i3−i3−i32-200-11-11−i3i3i3−i30000000000
χ362222-2-2-1-2-21111-1-1-1-2222-211-1-100001-1-11−i3−i3i3i3i3i3−i3−i3-22001-11-1i3−i3−i3i30000000000
χ372222-2-2-1-2-21111-1-1-1-2222-211-1-100001-1-11i3i3−i3−i3−i3−i3i3i32-200-11-11i3−i3−i3i30000000000
χ382222-2-2-1-2-21111-1-1-1-2222-211-1-100001-1-11i3i3−i3−i3−i3−i3i3i3-22001-11-1−i3i3i3−i30000000000
χ39444444-2-4-4-2-2-2-2-2-2-244-4-4-422220000-2-222000000000000000000000000000000
χ40444444-2-4-4-2-2-2-2-2-2-2-4-4-4442222000022-2-2000000000000000000000000000000
χ414444-4-4-2442222-2-2-24-4-44-4-2-2220000-22-22000000000000000000000000000000
χ424444-4-4-2442222-2-2-2-44-4-44-2-22200002-22-2000000000000000000000000000000
χ4344-4-44-440044-4-44-4-4000000000000000000000000000000000000000−2i22i2000000
χ4444-4-44-440044-4-44-4-40000000000000000000000000000000000000002i2−2i2000000
χ4544-4-4-44400-4-4444-4-40000000000000000000000000000000000000−2i22i200000000
χ4644-4-4-44400-4-4444-4-400000000000000000000000000000000000002i2−2i200000000
χ474-4-440044-40000-4-44000004-4002-22-200002-22-22-22-20000000000000000000000
χ484-4-440044-40000-4-44000004-400-22-220000-22-22-22-220000000000000000000000
χ494-4-44004-440000-4-4400000-44002-2-2200002-2-222-2-220000000000000000000000
χ504-4-44004-440000-4-4400000-4400-222-20000-222-2-222-20000000000000000000000
χ514-4-4400-24-4−2i32i3−2i32i322-200000-22−2i32i32-22-20000−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i30000000000000000000000
χ524-4-4400-24-4−2i32i3−2i32i322-200000-22−2i32i3-22-2200001+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i30000000000000000000000
χ534-4-4400-24-42i3−2i32i3−2i322-200000-222i3−2i32-22-20000−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i30000000000000000000000
χ544-4-4400-24-42i3−2i32i3−2i322-200000-222i3−2i3-22-2200001−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i30000000000000000000000
χ554-4-4400-2-44−2i32i3−2i32i322-2000002-22i3−2i32-2-220000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i30000000000000000000000
χ564-4-4400-2-44−2i32i3−2i32i322-2000002-22i3−2i3-222-200001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i30000000000000000000000
χ574-4-4400-2-442i3−2i32i3−2i322-2000002-2−2i32i32-2-220000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i30000000000000000000000
χ584-4-4400-2-442i3−2i32i3−2i322-2000002-2−2i32i3-222-200001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i30000000000000000000000
χ5988-8-88-8-400-4-444-44400000000000000000000000000000000000000000000000
χ6088-8-8-88-40044-4-4-44400000000000000000000000000000000000000000000000
χ618-88-8008000000-88-800000000000000000000000000000000000000000000000
χ628-88-800-400−4i34i34i3−4i34-4400000000000000000000000000000000000000000000000
χ638-88-800-4004i3−4i3−4i34i34-4400000000000000000000000000000000000000000000000

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