Finite Group Databasebeta

← Group #10768706

Character table — Group #10768706

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881616161616161616161624242424242424242424242424242424
order122222223446662444666666121212122444444412121212121212121212688121212242424242222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1111111-1-1-1-1
χ91111-1-1111-1-1111-1-11111-1-1-1-1-1-11111-1-111-1-11-11111-1-1-1-111-11-1-111-1-11-11-11-11-111-1-111-1-1
χ101111-1-1111-1-1111-1-11111-1-1-1-1-1-11111-1-111-1-11-11111-1-1-1-111-11-1-111-1-1-11-11-11-11-1-111-1-111
χ111111-1-1111-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-111111-111-1-1-1-1111-11-11-11-1-1-111-1-111
χ121111-1-1111-1-1111-1-11111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-111111-111-1-1-1-111-11-11-11-1111-1-111-1-1
χ131111-1-1111-1-1111-1-11111-1-1-1-1-1-111-1-11111-1-11-11111-1-1-1-1-1-11-111-1-1111-1-111-1-1111-1-1-1-111
χ141111-1-1111-1-1111-1-11111-1-1-1-1-1-111-1-11111-1-11-11111-1-1-1-1-1-11-111-1-111-111-1-111-1-1-11111-1-1
χ151111-1-1111-1-1111-1-11111-1-1-1-1-1-111-1-111-1-1111-1-1-1-1-11111-11-1-11111-1-11-1-111-1-11-1-11111-1-1
χ161111-1-1111-1-1111-1-11111-1-1-1-1-1-111-1-111-1-1111-1-1-1-1-11111-11-1-11111-1-1-111-1-111-111-1-1-1-111
χ17222222222-2-22222-2-2-2222222-2-2-2-200000000-2-20000000000000000002-200-220000000000
χ18222222222-2-22222-2-2-2222222-2-2-2-200000000-2-2000000000000000000-22002-20000000000
χ1922222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-10000000000000000
χ2022222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-2-2-1-1-111110000000000000000
χ2122222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-11-2-211111110000000000000000
χ2222222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111122111-1-1-1-10000000000000000
χ23222222-2-2222222-2-2-22-2-222-2-222-2-2000000002-2000000000000000000002200-2-200000000
χ24222222-2-2222222-2-2-22-2-222-2-222-2-2000000002-200000000000000000000-2-2002200000000
χ25222222-2-22-2-2222-222-2-2-222-2-2-2-2222-22-20000-2200000000200-22-200000000000000000000
χ26222222-2-22-2-2222-222-2-2-222-2-2-2-222-22-220000-2200000000-2002-2200000000000000000000
χ27222222-2-2-1-2-2-1-1-1-222-211-1-11111-1-12-22-200001-1−i3−i3i3i3−i3−i3i3i3-1001-11−i3i3−i3i30000000000000000
χ28222222-2-2-1-2-2-1-1-1-222-211-1-11111-1-12-22-200001-1i3i3−i3−i3i3i3−i3−i3-1001-11i3−i3i3−i30000000000000000
χ29222222-2-2-1-2-2-1-1-1-222-211-1-11111-1-1-22-2200001-1−i3−i3i3i3−i3−i3i3i3100-11-1i3−i3i3−i30000000000000000
χ30222222-2-2-1-2-2-1-1-1-222-211-1-11111-1-1-22-2200001-1i3i3−i3−i3i3i3−i3−i3100-11-1−i3i3−i3i30000000000000000
χ312222-2-222222222-22-2-222-2-2-2-222-2-200000000-220000000000000000002200-2-20000000000
χ322222-2-222222222-22-2-222-2-2-2-222-2-200000000-22000000000000000000-2-200220000000000
χ332222-2-222-1-2-2-1-1-1-2-222-1-1111111-1-122-2-222-2-2-11-1-1-1-11111-12-2-111-1-1110000000000000000
χ342222-2-222-1-2-2-1-1-1-2-222-1-1111111-1-122-2-2-2-222-111111-1-1-1-1-1-22-11111-1-10000000000000000
χ352222-2-222-1-2-2-1-1-1-2-222-1-1111111-1-1-2-22222-2-2-11-1-1-1-111111-221-1-111-1-10000000000000000
χ362222-2-222-1-2-2-1-1-1-2-222-1-1111111-1-1-2-222-2-222-111111-1-1-1-112-21-1-1-1-1110000000000000000
χ372222-2-2-2-22222222-22-2-2-2-2-22222222-2-220000-2-200000000200-2-2200000000000000000000
χ382222-2-2-2-22222222-22-2-2-2-2-2222222-222-20000-2-200000000-20022-200000000000000000000
χ392222-2-2-2-22-2-222222-22-2-2-2-222-2-2-2-20000000022000000000000000000002-200-2200000000
χ402222-2-2-2-22-2-222222-22-2-2-2-222-2-2-2-2000000002200000000000000000000-22002-200000000
χ412222-2-2-2-2-122-1-1-12-22-21111-1-1-1-1-1-12-2-22000011−i3−i3i3i3i3i3−i3−i3-10011-1−i3i3i3−i30000000000000000
χ422222-2-2-2-2-122-1-1-12-22-21111-1-1-1-1-1-12-2-22000011i3i3−i3−i3−i3−i3i3i3-10011-1i3−i3−i3i30000000000000000
χ432222-2-2-2-2-122-1-1-12-22-21111-1-1-1-1-1-1-222-2000011−i3−i3i3i3i3i3−i3−i3100-1-11i3−i3−i3i30000000000000000
χ442222-2-2-2-2-122-1-1-12-22-21111-1-1-1-1-1-1-222-2000011i3i3−i3−i3−i3−i3i3i3100-1-11−i3i3i3−i30000000000000000
χ4544444444-2-4-4-2-2-24-4-4-4-2-2-2-2-2-2222200000000220000000000000000000000000000000000
χ46444444-4-4-244-2-2-2-4-4-4422-2-222-2-22200000000-220000000000000000000000000000000000
χ474444-4-444-244-2-2-2-44-4-4-2-22222-2-222000000002-20000000000000000000000000000000000
χ484444-4-4-4-4-2-4-4-2-2-244-442222-2-2222200000000-2-20000000000000000000000000000000000
χ4944-4-4000044-4-4-4400000000004-40000002-22-2002-22-22-22-200000000000000000000000000
χ5044-4-4000044-4-4-4400000000004-4000000-22-2200-22-22-22-2200000000000000000000000000
χ5144-4-400004-44-4-440000000000-440000002-2-22002-22-2-22-2200000000000000000000000000
χ5244-4-400004-44-4-440000000000-44000000-222-200-22-222-22-200000000000000000000000000
χ5344-4-40000-24-422-200000000−2i32i3-22−2i32i300002-22-200−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i300000000000000000000000000
χ5444-4-40000-24-422-200000000−2i32i3-22−2i32i30000-22-22001+i3−1−i31−i3−1+i31−i3−1+i31+i3−1−i300000000000000000000000000
χ5544-4-40000-24-422-2000000002i3−2i3-222i3−2i300002-22-200−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i300000000000000000000000000
χ5644-4-40000-24-422-2000000002i3−2i3-222i3−2i30000-22-22001−i3−1+i31+i3−1−i31+i3−1−i31−i3−1+i300000000000000000000000000
χ5744-4-40000-2-4422-200000000−2i32i32-22i3−2i300002-2-2200−1+i31−i3−1−i31+i31+i3−1−i31−i3−1+i300000000000000000000000000
χ5844-4-40000-2-4422-200000000−2i32i32-22i3−2i30000-222-2001−i3−1+i31+i3−1−i3−1−i31+i3−1+i31−i300000000000000000000000000
χ5944-4-40000-2-4422-2000000002i3−2i32-2−2i32i300002-2-2200−1−i31+i3−1+i31−i31−i3−1+i31+i3−1−i300000000000000000000000000
χ6044-4-40000-2-4422-2000000002i3−2i32-2−2i32i30000-222-2001+i3−1−i31−i3−1+i3−1+i31−i3−1−i31+i300000000000000000000000000
χ614-44-4004-44004-4-400004-400000000000000000000000000000000000000000000000000−2i22i2
χ624-44-4004-44004-4-400004-4000000000000000000000000000000000000000000000000002i2−2i2
χ634-44-400-444004-4-40000-44000000000000000000000000000000000000000000000000−2i22i200
χ644-44-400-444004-4-40000-440000000000000000000000000000000000000000000000002i2−2i200
χ654-4-444-400400-44-40000004-40000000000000000000000000000000000000000002i−2i2i−2i0000
χ664-4-444-400400-44-40000004-4000000000000000000000000000000000000000000−2i2i−2i2i0000
χ674-4-44-4400400-44-4000000-440000000000000000000000000000000000000000002i−2i−2i2i0000
χ684-4-44-4400400-44-4000000-44000000000000000000000000000000000000000000−2i2i2i−2i0000
χ698-88-8008-8-400-4440000-440000000000000000000000000000000000000000000000000000
χ708-88-800-88-400-44400004-40000000000000000000000000000000000000000000000000000
χ718-8-888-800-4004-44000000-4400000000000000000000000000000000000000000000000000
χ728-8-88-8800-4004-440000004-400000000000000000000000000000000000000000000000000

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