Finite Group Databasebeta

← Group #10706298

Character table — Group #10706298

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order122222344446666666888822446666888888121212121212121224242424242424242424242424242424224466661212121216161616161616168888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111-1-11111111-1-1-1-1-1-11-1-1-1-1-11111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iii−i−i
χ6111111111-1-11111111-1-1-1-1-1-11-1-1-1-1-11111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−iii
χ7111111111-1-11111111-1-1-1-1-1-11-1-1-1-1-11111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−iii
χ8111111111-1-11111111-1-1-1-1-1-11-1-1-1-1-11111-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiii−i−i
χ91111-1-1111111-1-1-1-11111111-1-1-111-1-111-1-1-1-11-1-111-1-111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-111-1-11-11-1
χ101111-1-1111111-1-1-1-11111111-1-1-111-1-111-1-1-1-11-1-111-1-111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1-1-111-1-111-11-11
χ111111-1-1111111-1-1-1-11111111-1-1-111-1-111-1-1-1-11-1-111-1-111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-11111-1-111-1-1-11-11
χ121111-1-1111111-1-1-1-11111111-1-1-111-1-111-1-1-1-11-1-111-1-111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111-1-1111-11-1
χ131111-1-1111-1-11-1-1-1-111-1-1-1-1-11-11-1-11111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111ii−i−i−i−iiii−i−ii
χ141111-1-1111-1-11-1-1-1-111-1-1-1-1-11-11-1-11111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111−i−iiiii−i−i−iii−i
χ151111-1-1111-1-11-1-1-1-111-1-1-1-1-11-11-1-11111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1ii−i−i−i−iii−iii−i
χ161111-1-1111-1-11-1-1-1-111-1-1-1-1-11-11-1-11111-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1−i−iiiii−i−ii−i−ii
χ17222222222222222222-2-2-2-222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ18222222222-2-222222222222-2-22-2-2-2-2-2-2-2-2-222222-2-2-2-22-2-2-2-2-2-2-2-222222222000000000000000000000000
χ192222222-2-22222222220000-2-2-22-2-2-2-2000000-2-2-22222-200000000000000000000000000002−22−22−22−20000
χ202222222-2-22222222220000-2-2-22-2-2-2-2000000-2-2-22222-20000000000000000000000000000−22−22−22−220000
χ212222222-2-2-2-22222222000022-2-22222000000-2-2-2-2-2-2-2-20000000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ222222222-2-2-2-22222222000022-2-22222000000-2-2-2-2-2-2-2-20000000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ23222222-12222-1-1-1-1-1-1-122222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ24222222-12222-1-1-1-1-1-1-122222222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ27222222-122-2-2-1-1-1-1-1-1-12222-2-22-21111-2-2-2-222-1-1-11111-111111111-1-1-1-1-1-1-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ28222222-122-2-2-1-1-1-1-1-1-12222-2-22-21111-2-2-2-222-1-1-11111-111111111-1-1-1-1-1-1-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ29222222-122-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22-211112222-2-2-1-1-11111-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-11111000000000000
χ30222222-122-2-2-1-1-1-1-1-1-1-2-2-2-2-2-22-211112222-2-2-1-1-11111-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-1000000000000
χ312222-2-2222222-2-2-2-222-2-2-2-22-2-2-222-2-2-2-222222-2-222-2-22-2-2-2-22222-2-2-2-22222000000000000000000000000
χ322222-2-2222-2-22-2-2-2-2222222-22-22-2-222-2-222-2-22-2-2-2-2222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ332222-2-22-2-2222-2-2-2-2220000-222-2-2-222000000-22222-2-2-200000000000000000000000000002−2−222−2−220000
χ342222-2-22-2-2222-2-2-2-2220000-222-2-2-222000000-22222-2-2-20000000000000000000000000000−222−2−222−20000
χ352222-2-22-2-2-2-22-2-2-2-22200002-22222-2-2000000-222-2-222-20000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ362222-2-22-2-2-2-22-2-2-2-22200002-22222-2-2000000-222-2-222-20000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ372222-2-2-12222-11111-1-122222-2-2-2-1-11122-2-2-2-2-111-1-111-1-1-1-1-11111-1-1-1-111112-22-2-1-111-1-111000000000000
χ382222-2-2-12222-11111-1-122222-2-2-2-1-11122-2-2-2-2-111-1-111-1-1-1-1-11111-1-1-1-11111-22-2211-1-111-1-1000000000000
χ392222-2-2-12222-11111-1-1-2-2-2-22-2-2-2-1-111-2-22222-111-1-111-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3−i3i3i3−i3000000000000
χ402222-2-2-12222-11111-1-1-2-2-2-22-2-2-2-1-111-2-22222-111-1-111-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3i3−i3−i3i3000000000000
χ412222-2-2-122-2-2-11111-1-12222-22-2211-1-1-2-222-2-2-11111-1-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i3000000000000
χ422222-2-2-122-2-2-11111-1-12222-22-2211-1-1-2-222-2-2-11111-1-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i3000000000000
χ432222-2-2-122-2-2-11111-1-1-2-2-2-2-22-2211-1-122-2-222-11111-1-1-1-1-1-1-111111111-1-1-1-12-2-22-1-11111-1-1000000000000
χ442222-2-2-122-2-2-11111-1-1-2-2-2-2-22-2211-1-122-2-222-11111-1-1-1-1-1-1-111111111-1-1-1-1-222-211-1-1-1-111000000000000
χ45444444-2-4-444-2-2-2-2-2-2-20000-4-4-442222000000222-2-2-2-220000000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2-2-2-2-2000044-4-4-2-2-2-2000000222222220000000000000000000000000000000000000000
χ474444-4-4-2-4-444-22222-2-20000-444-422-2-20000002-2-2-2-22220000000000000000000000000000000000000000
χ484444-4-4-2-4-4-4-4-22222-2-200004-444-2-2220000002-2-222-2-220000000000000000000000000000000000000000
χ4944-4-4004004i−4i40000-4-4−2i2−2i22i22i20000000022−2200000004i−4i0002222−22−220000−2i2−2i22i22i20000000000000000000000000000
χ5044-4-4004004i−4i40000-4-42i22i2−2i2−2i200000000−222200000004i−4i000−22−22222200002i22i2−2i2−2i20000000000000000000000000000
χ5144-4-400400−4i4i40000-4-4−2i2−2i22i22i200000000−22220000000−4i4i000−22−2222220000−2i2−2i22i22i20000000000000000000000000000
χ5244-4-400400−4i4i40000-4-42i22i2−2i2−2i20000000022−220000000−4i4i0002222−22−2200002i22i2−2i2−2i20000000000000000000000000000
χ5344-4-400-2004i−4i-2−2i3−2i32i32i322−2i2−2i22i22i20000000022−220000000−2i2i23−230−2−222i6i6−i6−i6i2i2−i2−i266−6−6000000000000000000000000
χ5444-4-400-2004i−4i-2−2i3−2i32i32i3222i22i2−2i2−2i200000000−22220000000−2i2i23−23022−2−2−i6−i6i6i6−i2−i2i2i2−6−666000000000000000000000000
χ5544-4-400-2004i−4i-22i32i3−2i3−2i322−2i2−2i22i22i20000000022−220000000−2i2i−23230−2−222−i6−i6i6i6i2i2−i2−i2−6−666000000000000000000000000
χ5644-4-400-2004i−4i-22i32i3−2i3−2i3222i22i2−2i2−2i200000000−22220000000−2i2i−2323022−2−2i6i6−i6−i6−i2−i2i2i266−6−6000000000000000000000000
χ5744-4-400-200−4i4i-2−2i3−2i32i32i322−2i2−2i22i22i200000000−222200000002i−2i−2323022−2−2−i6−i6i6i6i2i2−i2−i266−6−6000000000000000000000000
χ5844-4-400-200−4i4i-2−2i3−2i32i32i3222i22i2−2i2−2i20000000022−2200000002i−2i−23230−2−222i6i6−i6−i6−i2−i2i2i2−6−666000000000000000000000000
χ5944-4-400-200−4i4i-22i32i3−2i3−2i322−2i2−2i22i22i200000000−222200000002i−2i23−23022−2−2i6i6−i6−i6i2i2−i2−i2−6−666000000000000000000000000
χ6044-4-400-200−4i4i-22i32i3−2i3−2i3222i22i2−2i2−2i20000000022−2200000002i−2i23−230−2−222−i6−i6i6i6−i2−i2i2i266−6−6000000000000000000000000
χ614-44-40044-400-400004-44i−4i4i−4i000000000000004000000-4000000004i−4i4i−4i0000000000000000000000000000
χ624-44-40044-400-400004-4−4i4i−4i4i000000000000004000000-400000000−4i4i−4i4i0000000000000000000000000000
χ634-44-4004-4400-400004-4000000000000004-400-4000000400004-44-400000000000000000000000000000000
χ644-44-4004-4400-400004-400000000000000-4400-400000040000-44-4400000000000000000000000000000000
χ654-44-400-24-4002−2i32i3−2i32i3-224i−4i4i−4i00000000000000-2−2i32i30000200000000−2i2i−2i2i23−2323−23000000000000000000000000
χ664-44-400-24-4002−2i32i3−2i32i3-22−4i4i−4i4i00000000000000-2−2i32i300002000000002i−2i2i−2i−2323−2323000000000000000000000000
χ674-44-400-24-40022i3−2i32i3−2i3-224i−4i4i−4i00000000000000-22i3−2i30000200000000−2i2i−2i2i−2323−2323000000000000000000000000
χ684-44-400-24-40022i3−2i32i3−2i3-22−4i4i−4i4i00000000000000-22i3−2i300002000000002i−2i2i−2i23−2323−23000000000000000000000000
χ694-44-400-2-44002−2i32i3−2i32i3-22000000000000004-40022i3−2i30000-2−2i32i3−2i32i3-22-2200000000000000000000000000000000
χ704-44-400-2-44002−2i32i3−2i32i3-2200000000000000-440022i3−2i30000-22i3−2i32i3−2i32-22-200000000000000000000000000000000
χ714-44-400-2-440022i3−2i32i3−2i3-22000000000000004-4002−2i32i30000-22i3−2i32i3−2i3-22-2200000000000000000000000000000000
χ724-44-400-2-440022i3−2i32i3−2i3-2200000000000000-44002−2i32i30000-2−2i32i3−2i32i32-22-200000000000000000000000000000000
χ734-4-444-440000-44-4-44-4422−22−222200000000000022−22000000000000000022−22−2222−222222−22000000000000000000000000
χ744-4-444-440000-44-4-44-44−222222−22000000000000−22220000000000000000−222222−2222−22−2222000000000000000000000000
χ754-4-444-4-200002-222-22-222−22−22220000−2i32i3−2i32i3000022−2200000000i6−i6−i6i6−i6i6i6−i6−222−22−2−22000000000000000000000000
χ764-4-444-4-200002-222-22-222−22−222200002i3−2i32i3−2i3000022−2200000000−i6i6i6−i6i6−i6−i6i6−222−22−2−22000000000000000000000000
χ774-4-444-4-200002-222-22-2−222222−220000−2i32i3−2i32i30000−222200000000−i6i6i6−i6i6−i6−i6i62−2−22−222−2000000000000000000000000
χ784-4-444-4-200002-222-22-2−222222−2200002i3−2i32i3−2i30000−222200000000i6−i6−i6i6−i6i6i6−i62−2−22−222−2000000000000000000000000
χ794-4-44-4440000-4-444-4-4422−22−2222000000000000−2222000000000000000022−22−222222−22−2222000000000000000000000000
χ804-4-44-4440000-4-444-4-44−222222−2200000000000022−220000000000000000−222222−22−222222−22000000000000000000000000
χ814-4-44-44-2000022-2-222-222−22−22220000−2i32i32i3−2i30000−222200000000i6−i6−i6i6i6−i6−i6i6−222−2−222−2000000000000000000000000
χ824-4-44-44-2000022-2-222-222−22−222200002i3−2i3−2i32i30000−222200000000−i6i6i6−i6−i6i6i6−i6−222−2−222−2000000000000000000000000
χ834-4-44-44-2000022-2-222-2−222222−220000−2i32i32i3−2i3000022−2200000000−i6i6i6−i6−i6i6i6−i62−2−222−2−22000000000000000000000000
χ844-4-44-44-2000022-2-222-2−222222−2200002i3−2i3−2i32i3000022−2200000000i6−i6−i6i6i6−i6−i6i62−2−222−2−22000000000000000000000000

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