Finite Group Databasebeta

← Group #10770417

Character table — Group #10770417

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888161616161616161616162424242424242424242424244848
order12222234466644444661212121212121212444488881212242424242424242444121212121212121224444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1
χ6111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-11-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-111-1111111-1-1
χ91111111-1-1111-1-1-11111-1-1-1-1-1-1111-11-111-1-11-11111-1-1-1-11-111-1-111-1-11-1-11-111-111-1-11-1
χ101111111-1-1111-1-1-11111-1-1-1-1-1-1111-11-111-1-11-11111-1-1-1-11-111-1-111-1-1-111-11-1-11-1-111-11
χ111111111-1-1111-1-1-11111-1-1-1-1-1-1111-11-1-1-1111-1-1-1-1-11111-1111-1-1-1-1111-1-11-111-1-1-111-11
χ121111111-1-1111-1-1-11111-1-1-1-1-1-1111-11-1-1-1111-1-1-1-1-11111-1111-1-1-1-111-111-11-1-1111-1-11-1
χ131111111-1-1111-1-1-11111-1-1-1-1-1-111-11-1111-1-11-11111-1-1-1-1-11-1-111-1-1111-1-1-111-1111-1-1-11
χ141111111-1-1111-1-1-11111-1-1-1-1-1-111-11-1111-1-11-11111-1-1-1-1-11-1-111-1-111-1111-1-11-1-1-1111-1
χ151111111-1-1111-1-1-11111-1-1-1-1-1-111-11-11-1-1111-1-1-1-1-111111-1-1-11111-1-11-1-1-111-11-1-1111-1
χ161111111-1-1111-1-1-11111-1-1-1-1-1-111-11-11-1-1111-1-1-1-1-111111-1-1-11111-1-1-1111-1-11-111-1-1-11
χ172222222222222-2-2-2-22222-2-2-2-2-2-200000000-22000000000000000000000220-2-2000000
χ182222222222222-2-2-2-22222-2-2-2-2-2-200000000-22000000000000000000000-2-2022000000
χ192222222-2-2222-222-2-222-2-22222-2-200000000-2-20000000000000000000002-20-22000000
χ202222222-2-2222-222-2-222-2-22222-2-200000000-2-2000000000000000000000-2202-2000000
χ21222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000
χ22222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-2-2-1-1-1-1111100000000000000
χ23222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-2-21111111100000000000000
χ24222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111221111-1-1-1-100000000000000
χ25222222-1-2-2-1-1-1-2-2-222-1-1111111-1-12-22-222-2-2-11-1-1-1-111112-2-1-111-1-11100000000000000
χ26222222-1-2-2-1-1-1-2-2-222-1-1111111-1-12-22-2-2-222-111111-1-1-1-1-22-1-11111-1-100000000000000
χ27222222-1-2-2-1-1-1-2-2-222-1-1111111-1-1-22-2222-2-2-11-1-1-1-11111-2211-1-111-1-100000000000000
χ28222222-1-2-2-1-1-1-2-2-222-1-1111111-1-1-22-22-2-222-111111-1-1-1-12-211-1-1-1-11100000000000000
χ292222-2-2222222-22-22-2-2-22222-2-22222-2-20000-2-200000000002-22-2000000000000000000
χ302222-2-2222222-22-22-2-2-22222-2-222-2-2220000-2-20000000000-22-22000000000000000000
χ312222-2-2222222-2-22-22-2-222-2-222-2-2000000002-200000000000000000022-200-200000000
χ322222-2-2222222-2-22-22-2-222-2-222-2-2000000002-2000000000000000000-2-2200200000000
χ332222-2-22-2-222222-2-22-2-2-2-222-2-2-2-200000000220000000000000000002-2200-200000000
χ342222-2-22-2-222222-2-22-2-2-2-222-2-2-2-20000000022000000000000000000-22-200200000000
χ352222-2-22-2-22222-222-2-2-2-2-2-2-222222-2-220000-2200000000002-2-22000000000000000000
χ362222-2-22-2-22222-222-2-2-2-2-2-2-22222-222-20000-220000000000-222-2000000000000000000
χ372222-2-2-122-1-1-1-22-22-211-1-1-1-111-1-122-2-2000011−i3−i3i3i3−i3−i3i3i300-11-11−i3i3−i3i300000000000000
χ382222-2-2-122-1-1-1-22-22-211-1-1-1-111-1-122-2-2000011i3i3−i3−i3i3i3−i3−i300-11-11i3−i3i3−i300000000000000
χ392222-2-2-122-1-1-1-22-22-211-1-1-1-111-1-1-2-222000011−i3−i3i3i3−i3−i3i3i3001-11-1i3−i3i3−i300000000000000
χ402222-2-2-122-1-1-1-22-22-211-1-1-1-111-1-1-2-222000011i3i3−i3−i3i3i3−i3−i3001-11-1−i3i3−i3i300000000000000
χ412222-2-2-1-2-2-1-1-12-222-2111111-1-1-1-12-2-2200001-1−i3−i3i3i3i3i3−i3−i300-111-1−i3i3i3−i300000000000000
χ422222-2-2-1-2-2-1-1-12-222-2111111-1-1-1-12-2-2200001-1i3i3−i3−i3−i3−i3i3i300-111-1i3−i3−i3i300000000000000
χ432222-2-2-1-2-2-1-1-12-222-2111111-1-1-1-1-222-200001-1−i3−i3i3i3i3i3−i3−i3001-1-11i3−i3−i3i300000000000000
χ442222-2-2-1-2-2-1-1-12-222-2111111-1-1-1-1-222-200001-1i3i3−i3−i3−i3−i3i3i3001-1-11−i3i3i3−i300000000000000
χ45444444-244-2-2-24-4-4-4-4-2-2-2-2222222000000002-200000000000000000000000000000000
χ46444444-2-4-4-2-2-2-444-4-4-2-222-2-2-2-222000000002200000000000000000000000000000000
χ474444-4-4-244-2-2-2-4-44-4422-2-222-2-22200000000-2200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-244-4-442222-2-2222200000000-2-200000000000000000000000000000000
χ4944-4-40044-44-4-400000004-40000000000000000000000000000000000000000002-22-200
χ5044-4-40044-44-4-400000004-4000000000000000000000000000000000000000000-22-2200
χ5144-4-4004-444-4-40000000-440000000000000000000000000000000000000000002-2-2200
χ5244-4-4004-444-4-40000000-44000000000000000000000000000000000000000000-222-200
χ534-4-444-4400-4-44000004-400000000000000−2i22i2000000−2i22i2−2i22i2000000000000000000000000
χ544-4-444-4400-4-44000004-4000000000000002i2−2i20000002i2−2i22i2−2i2000000000000000000000000
χ554-4-444-4-20022-200000-2200−2i32i3−2i32i300000000−2i22i2006−66−6i2−i2i2−i2000000000000000000000000
χ564-4-444-4-20022-200000-2200−2i32i3−2i32i3000000002i2−2i200−66−66−i2i2−i2i2000000000000000000000000
χ574-4-444-4-20022-200000-22002i3−2i32i3−2i300000000−2i22i200−66−66i2−i2i2−i2000000000000000000000000
χ584-4-444-4-20022-200000-22002i3−2i32i3−2i3000000002i2−2i2006−66−6−i2i2−i2i2000000000000000000000000
χ594-4-44-44400-4-4400000-44000000000000−2i22i20000−2i22i22i2−2i20000000000000000000000000000
χ604-4-44-44400-4-4400000-440000000000002i2−2i200002i2−2i2−2i22i20000000000000000000000000000
χ614-4-44-44-20022-2000002-200−2i32i32i3−2i3000000−2i22i20000i2−i2−i2i26−6−66000000000000000000000000
χ624-4-44-44-20022-2000002-200−2i32i32i3−2i30000002i2−2i20000−i2i2i2−i2−666−6000000000000000000000000
χ634-4-44-44-20022-2000002-2002i3−2i3−2i32i3000000−2i22i20000i2−i2−i2i2−666−6000000000000000000000000
χ644-4-44-44-20022-2000002-2002i3−2i3−2i32i30000002i2−2i20000−i2i2i2−i26−6−66000000000000000000000000
χ6588-8-800-48-8-4440000000-44000000000000000000000000000000000000000000000000
χ6688-8-800-4-88-44400000004-4000000000000000000000000000000000000000000000000
χ678-88-800800-88-8000000000000000000000000000000000000000000000000000000000
χ688-88-800-4004-440000000000000−4i34i3000000000000000000000000000000000000000000
χ698-88-800-4004-4400000000000004i3−4i3000000000000000000000000000000000000000000

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