Finite Group Databasebeta

← Group #10829217

Character table — Group #10829217

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order122222223444444446666666441212121212121212444444448888121212121212121212122424242424242424224444448888888812121212244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ9111111111-1-1-1-111111111111-1-1111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-11111-1
χ10111111111-1-1-1-111111111111-1-1111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-11-1-1-1-11
χ11111111111-1-1-1-111111111111-1-1111-1-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-11
χ12111111111-1-1-1-111111111111-1-1111-1-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-11-1-1-11-1
χ13111111111-1-1-1-111111111111-1-1111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-111-11-1-11-1
χ14111111111-1-1-1-111111111111-1-1111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111-111-11
χ15111111111-1-1-1-111111111111-1-1111-1-1-1-11-1-111-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111-11-1-1-11
χ16111111111-1-1-1-111111111111-1-1111-1-1-1-11-1-111-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-1111-1
χ172222222222222-2-2-2-22222222-2-2-2-2-22222-20000000000000000-2-200000000000022000022000000000000-2-20000
χ182222222222222-2-2-2-22222222-2-2-2-2-22222-20000000000000000-2-2000000000000-2-20000-2-2000000000000220000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000000022000000000000220000-2-20000000000002-20000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000000022000000000000-2-2000022000000000000-220000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-21111-1-11111111111110000000000000000-1-1-1-1000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000000000001111000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111-1-11111-1-1-1-1-1-1-1-100000000000000001111000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-222-2-222-2-2111111-1-1-1-1-1-1-1-111110000000000000000-1-111000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-2-222-2-222-1-1-1-11111111111-1-1-1-10000000000000000-1-111000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-22222-2-2-2-222111111-1-1-1-11111-1-1-1-1000000000000000011-1-1000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-222-2-22222-2-2-1-1-1-1111111-1-1-1-11111000000000000000011-1-1000000
χ29222-2-2-2-2220000-222-222-2-22-2-2002-2-20000200002i−2i0000000000002i2i−2i−2i00000000002i2i−2i−2i00000022-2-20000000000
χ30222-2-2-2-2220000-222-222-2-22-2-2002-2-20000200002i−2i0000000000002i2i−2i−2i0000000000−2i−2i2i2i000000-2-2220000000000
χ31222-2-2-2-2220000-222-222-2-22-2-2002-2-2000020000−2i2i000000000000−2i−2i2i2i00000000002i2i−2i−2i000000-2-2220000000000
χ32222-2-2-2-2220000-222-222-2-22-2-2002-2-2000020000−2i2i000000000000−2i−2i2i2i0000000000−2i−2i2i2i00000022-2-20000000000
χ3322-2-22-22-222i2i−2i−2i00002-22-2-2-22000002i2i−2i−2i000000000−i2i22−20000000000−i2−i2i2i222−2−22-200002i−2i−i2−i2i2i22−22−20000000000
χ3422-2-22-22-222i2i−2i−2i00002-22-2-2-22000002i2i−2i−2i000000000−i2i22−20000000000−i2−i2i2i222−2−2-220000−2i2ii2i2−i2−i2−22−220000000000
χ3522-2-22-22-222i2i−2i−2i00002-22-2-2-22000002i2i−2i−2i000000000i2−i2−220000000000i2i2−i2−i2−2−2222-200002i−2ii2i2−i2−i2−22−220000000000
χ3622-2-22-22-222i2i−2i−2i00002-22-2-2-22000002i2i−2i−2i000000000i2−i2−220000000000i2i2−i2−i2−2−222-220000−2i2i−i2−i2i2i22−22−20000000000
χ3722-2-22-22-22−2i−2i2i2i00002-22-2-2-2200000−2i−2i2i2i000000000−i2i2−220000000000−i2−i2i2i2−2−2222-20000−2i2i−i2−i2i2i2−22−220000000000
χ3822-2-22-22-22−2i−2i2i2i00002-22-2-2-2200000−2i−2i2i2i000000000−i2i2−220000000000−i2−i2i2i2−2−222-2200002i−2ii2i2−i2−i22−22−20000000000
χ3922-2-22-22-22−2i−2i2i2i00002-22-2-2-2200000−2i−2i2i2i000000000i2−i22−20000000000i2i2−i2−i222−2−22-20000−2i2ii2i2−i2−i22−22−20000000000
χ4022-2-22-22-22−2i−2i2i2i00002-22-2-2-2200000−2i−2i2i2i000000000i2−i22−20000000000i2i2−i2−i222−2−2-2200002i−2i−i2−i2i2i2−22−220000000000
χ412-2-22-2-22222-22-222-2-2-2-2-2-22222-2-22-22-22-222-22-20000000000002-200000000000000000000000000002-22-2000000
χ422-2-22-2-22222-22-222-2-2-2-2-2-22222-2-22-22-22-22-22-220000000000002-20000000000000000000000000000-22-22000000
χ432-2-22-2-22222-22-2-2-222-2-2-2-2222-222-222-22-2-20000000000000000-22000000000000002-22-200000000000000002-200
χ442-2-22-2-22222-22-2-2-222-2-2-2-2222-222-222-22-2-20000000000000000-2200000000000000-22-220000000000000000-2200
χ452-2-22-2-2222-22-2222-2-2-2-2-2-2222-22-22-2-22-2222-2-22000000000000-2200000000000000000000000000002-2-22000000
χ462-2-22-2-2222-22-2222-2-2-2-2-2-2222-22-22-2-22-222-222-2000000000000-220000000000000000000000000000-222-2000000
χ472-2-22-2-2222-22-22-2-222-2-2-2-22222-22-22-22-22-200000000000000002-2000000000000002-22-20000000000000000-2200
χ482-2-22-2-2222-22-22-2-222-2-2-2-22222-22-22-22-22-200000000000000002-200000000000000-22-2200000000000000002-200
χ492-2-22-2-222-12-22-222-2-21111-1-1-12-21-11-11-11-12-22-200000000−i3−i3i3i3-11−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000-11-11000000
χ502-2-22-2-222-12-22-222-2-21111-1-1-12-21-11-11-11-12-22-200000000i3i3−i3−i3-11i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000-11-11000000
χ512-2-22-2-222-12-22-222-2-21111-1-1-12-21-11-11-11-1-22-2200000000−i3−i3i3i3-11−i3i3−i3i3i3−i3i3−i3i3−i3i3−i300000000000000001-11-1000000
χ522-2-22-2-222-12-22-222-2-21111-1-1-12-21-11-11-11-1-22-2200000000i3i3−i3−i3-11i3−i3i3−i3−i3i3−i3i3−i3i3−i3i300000000000000001-11-1000000
χ532-2-22-2-222-1-22-2222-2-21111-1-1-1-221-111-11-1-12-2-2200000000−i3−i3i3i31-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i30000000000000000-111-1000000
χ542-2-22-2-222-1-22-2222-2-21111-1-1-1-221-111-11-1-12-2-2200000000i3i3−i3−i31-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i30000000000000000-111-1000000
χ552-2-22-2-222-1-22-2222-2-21111-1-1-1-221-111-11-1-1-222-200000000−i3−i3i3i31-1i3−i3i3−i3−i3i3−i3i3i3−i3i3−i300000000000000001-1-11000000
χ562-2-22-2-222-1-22-2222-2-21111-1-1-1-221-111-11-1-1-222-200000000i3i3−i3−i31-1−i3i3−i3i3i3−i3i3−i3−i3i3−i3i300000000000000001-1-11000000
χ572-2-2-222-22200002-22-2-2-2222-2-20022-20000-20000002-200002-22-200000000000000002i−2i−2i2i002i−2i2i−2i00000000000000
χ582-2-2-222-22200002-22-2-2-2222-2-20022-20000-20000002-200002-22-20000000000000000−2i2i2i−2i00−2i2i−2i2i00000000000000
χ592-2-2-222-22200002-22-2-2-2222-2-20022-20000-2000000-220000-22-2200000000000000002i−2i−2i2i00−2i2i−2i2i00000000000000
χ602-2-2-222-22200002-22-2-2-2222-2-20022-20000-2000000-220000-22-220000000000000000−2i2i2i−2i002i−2i2i−2i00000000000000
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000000000002200000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000000000000000-2-200000000000000000000000000000000000000
χ63444-4-4-4-44400004-4-4444-4-44-4-400-4440000-400000000000000000000000000000000000000000000000000000000
χ64444-4-4-4-44-200004-4-44-2-222-222002-2-200002000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ65444-4-4-4-44-200004-4-44-2-222-222002-2-2000020000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ66444-4-4-4-44-20000-444-4-2-222-22200-2220000-200004i−4i000000000000−2i−2i2i2i0000000000000000000000000000000000
χ67444-4-4-4-44-20000-444-4-2-222-22200-2220000-20000−4i4i0000000000002i2i−2i−2i0000000000000000000000000000000000
χ6844-44-44-4-44000000004-4-44-44-4000000000000000000000000000000000000000000000000000022−22−22220000000000
χ6944-44-44-4-44000000004-4-44-44-40000000000000000000000000000000000000000000000000000−222222−220000000000
χ7044-4-44-44-4-24i4i−4i−4i0000-22-2222-200000−2i−2i2i2i000000000−2i22i222−220000000000i2i2−i2−i2−2−22200000000000000000000000000
χ7144-4-44-44-4-24i4i−4i−4i0000-22-2222-200000−2i−2i2i2i0000000002i2−2i2−22220000000000−i2−i2i2i222−2−200000000000000000000000000
χ7244-4-44-44-4-2−4i−4i4i4i0000-22-2222-2000002i2i−2i−2i000000000−2i22i2−22220000000000i2i2−i2−i222−2−200000000000000000000000000
χ7344-4-44-44-4-2−4i−4i4i4i0000-22-2222-2000002i2i−2i−2i0000000002i2−2i222−220000000000−i2−i2i2i2−2−22200000000000000000000000000
χ744-4444-4-4-4400000000-444-4-44-400000000000000000000000000000000000000000000000022−22−222200000000000000
χ754-4444-4-4-4400000000-444-4-44-4000000000000000000000000000000000000000000000000−222222−2200000000000000
χ764-44-4-444-444i−4i−4i4i0000-44-44-4-44000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000
χ774-44-4-444-44−4i4i4i−4i0000-44-44-4-4400000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000
χ784-44-4-444-4-24i−4i−4i4i00002-22-222-200000−2i2i2i−2i000000000000000000000006−6−66i6−i6−i6i600000000000000000000000000
χ794-44-4-444-4-24i−4i−4i4i00002-22-222-200000−2i2i2i−2i00000000000000000000000−666−6−i6i6i6−i600000000000000000000000000
χ804-44-4-444-4-2−4i4i4i−4i00002-22-222-2000002i−2i−2i2i000000000000000000000006−6−66−i6i6i6−i600000000000000000000000000
χ814-44-4-444-4-2−4i4i4i−4i00002-22-222-2000002i−2i−2i2i00000000000000000000000−666−6i6−i6−i6i600000000000000000000000000
χ824-4-44-4-444-24-44-4-4-4442222-2-2-2-44-22-2-22-22200000000000000002-200000000000000000000000000000000000000
χ834-4-44-4-444-2-44-44-4-4442222-2-2-24-4-22-22-22-220000000000000000-2200000000000000000000000000000000000000
χ844-4-4-444-4440000-44-44-4-4444-4-400-4-440000400000000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-200004-44-422-2-2-22200-2-22000020000004-40000-22-220000000000000000000000000000000000000000
χ864-4-4-444-44-200004-44-422-2-2-22200-2-2200002000000-4400002-22-20000000000000000000000000000000000000000
χ874-4-4-444-44-20000-44-4422-2-2-2220022-20000-200000000000000000023−23−23230000000000000000000000000000000000
χ884-4-4-444-44-20000-44-4422-2-2-2220022-20000-2000000000000000000−232323−230000000000000000000000000000000000
χ8988-88-88-8-8-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8888-8-8-8-4000000004-4-444-44000000000000000000000000000000000000000000000000000000000000000000

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