Finite Group Databasebeta

← Group #10845167

Character table — Group #10845167

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order1222222234444444466666664412121212121212122244444488881212121212121212121224242424242424244444444488888888661212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-11-1-11-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ911111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-11
χ1011111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-111-1-11-1-1-11-1
χ1111111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1-11111-1
χ1211111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1111111-1-11-1-1-1-11
χ1311111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111111111-1-1-1-1-1-111-1-1-11-11
χ1411111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111111-11-1
χ1511111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-111-1
χ1611111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111-1-11
χ17222222222-2-22222-2-22222222-2-22222-2-2-2-2000000000000-2-2000000000000000022220000000000000000-200-200
χ18222222222-2-22222-2-22222222-2-22222-2-2-2-2000000000000-2-20000000000000000-2-2-2-20000000000000000200200
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000000022000000000000000022-2-20000000000000000200-200
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000220000000000000000-2-2220000000000000000-200200
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
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-111111111111111110000000000000000-1-1-1-1000000
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
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000000000001111000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-222-2-222-2-2111111-1-1-1-1-1-1-1-111110000000000000000-1-111000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-2-2-222-2-22211-1-1-1-111111111-1-1-1-10000000000000000-1-111000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-22222-2-2-2-222111111-1-1-1-11111-1-1-1-1000000000000000011-1-1000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-222-2-22222-2-211-1-1-1-11111-1-1-1-11111000000000000000011-1-1000000
χ292222-2-2-2-222-20000-2222-2-2-2-220000002-2-2200002-200000000000022-2-20000000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ302222-2-2-2-222-20000-2222-2-2-2-220000002-2-2200002-200000000000022-2-2000000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ312222-2-2-2-222-20000-2222-2-2-2-220000002-2-220000-22000000000000-2-2220000000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ322222-2-2-2-222-20000-2222-2-2-2-220000002-2-220000-22000000000000-2-222000000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ3322-2-2-2-2222002i2i−2i−2i002-22-2-22-2002i2i−2i−2i000000000000−i2i22−20000000000−i2−i2i2i222−2−22i−2i2-20000−i2i2−i2i222−2−20000000000
χ3422-2-2-2-2222002i2i−2i−2i002-22-2-22-2002i2i−2i−2i000000000000−i2i22−20000000000−i2−i2i2i222−2−2−2i2i-220000i2−i2i2−i2−2−2220000000000
χ3522-2-2-2-2222002i2i−2i−2i002-22-2-22-2002i2i−2i−2i000000000000i2−i2−220000000000i2i2−i2−i2−2−2222i−2i2-20000i2−i2i2−i2−2−2220000000000
χ3622-2-2-2-2222002i2i−2i−2i002-22-2-22-2002i2i−2i−2i000000000000i2−i2−220000000000i2i2−i2−i2−2−222−2i2i-220000−i2i2−i2i222−2−20000000000
χ3722-2-2-2-222200−2i−2i2i2i002-22-2-22-200−2i−2i2i2i000000000000−i2i2−220000000000−i2−i2i2i2−2−2222i−2i-220000i2−i2i2−i222−2−20000000000
χ3822-2-2-2-222200−2i−2i2i2i002-22-2-22-200−2i−2i2i2i000000000000−i2i2−220000000000−i2−i2i2i2−2−222−2i2i2-20000−i2i2−i2i2−2−2220000000000
χ3922-2-2-2-222200−2i−2i2i2i002-22-2-22-200−2i−2i2i2i000000000000i2−i22−20000000000i2i2−i2−i222−2−22i−2i-220000−i2i2−i2i2−2−2220000000000
χ4022-2-2-2-222200−2i−2i2i2i002-22-2-22-200−2i−2i2i2i000000000000i2−i22−20000000000i2i2−i2−i222−2−2−2i2i2-20000i2−i2i2−i222−2−20000000000
χ412-22-22-2-2222-200002-2-2-222-2-2200000022-2-20000002i−2i0000002i2i−2i−2i00000000000000002-22-200002i−2i2i−2i0000000000
χ422-22-22-2-2222-200002-2-2-222-2-2200000022-2-20000002i−2i0000002i2i−2i−2i0000000000000000-22-220000−2i2i−2i2i0000000000
χ432-22-22-2-2222-200002-2-2-222-2-2200000022-2-2000000−2i2i000000−2i−2i2i2i00000000000000002-22-20000−2i2i−2i2i0000000000
χ442-22-22-2-2222-200002-2-2-222-2-2200000022-2-2000000−2i2i000000−2i−2i2i2i0000000000000000-22-2200002i−2i2i−2i0000000000
χ452-22-2-222-22222-22-2-2-2-2-2-2-22222-22-22-22-22-20000000000002-2000000000000000000002i−2i−2i2i00000000000002i−2i000
χ462-22-2-222-22222-22-2-2-2-2-2-2-22222-22-22-22-22-20000000000002-200000000000000000000−2i2i2i−2i0000000000000−2i2i000
χ472-22-2-222-2222-22-22-2-2-2-2-2-2222-22-22-222-22-2000000000000-22000000000000000000002i−2i−2i2i0000000000000−2i2i000
χ482-22-2-222-2222-22-22-2-2-2-2-2-2222-22-22-222-22-2000000000000-2200000000000000000000−2i2i2i−2i00000000000002i−2i000
χ492-22-2-222-22-2-22-22-222-2-2-2-2222-222-22-2-22-222-22-200000000-22000000000000000000000000000000002-22-2000000
χ502-22-2-222-22-2-22-22-222-2-2-2-2222-222-22-2-22-22-22-2200000000-2200000000000000000000000000000000-22-22000000
χ512-22-2-222-22-2-2-22-2222-2-2-2-22222-2-22-22-22-222-2-22000000002-2000000000000000000000000000000002-2-22000000
χ522-22-2-222-22-2-2-22-2222-2-2-2-22222-2-22-22-22-22-222-2000000002-200000000000000000000000000000000-222-2000000
χ532-22-2-222-2-1-2-22-22-2221111-1-1-1-22-11-111-11-12-22-2000000001-1−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000-11-11000000
χ542-22-2-222-2-1-2-22-22-2221111-1-1-1-22-11-111-11-12-22-2000000001-1i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000-11-11000000
χ552-22-2-222-2-1-2-22-22-2221111-1-1-1-22-11-111-11-1-22-22000000001-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i300000000000000001-11-1000000
χ562-22-2-222-2-1-2-22-22-2221111-1-1-1-22-11-111-11-1-22-22000000001-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i300000000000000001-11-1000000
χ572-22-2-222-2-1-2-2-22-22221111-1-1-12-21-11-11-11-12-2-2200000000-11−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3−i3i3−i3i30000000000000000-111-1000000
χ582-22-2-222-2-1-2-2-22-22221111-1-1-12-21-11-11-11-12-2-2200000000-11i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3i3−i3i3−i30000000000000000-111-1000000
χ592-22-2-222-2-1-2-2-22-22221111-1-1-12-21-11-11-11-1-222-200000000-11−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i300000000000000001-1-11000000
χ602-22-2-222-2-1-2-2-22-22221111-1-1-12-21-11-11-11-1-222-200000000-11i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i300000000000000001-1-11000000
χ6144444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000000022000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000000000
χ634444-4-4-4-44-4400004-444-4-4-4-44000000-444-400000000000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-24-40000-44-2-22222-2000000-222-200004-4000000000000-2-2220000000000000000000000000000000000
χ654444-4-4-4-4-24-40000-44-2-22222-2000000-222-20000-4400000000000022-2-20000000000000000000000000000000000
χ664444-4-4-4-4-2-4400004-4-2-22222-20000002-2-220000000000000023−23−232300000000000000000000000000000000000000
χ674444-4-4-4-4-2-4400004-4-2-22222-20000002-2-2200000000000000−232323−2300000000000000000000000000000000000000
χ6844-4-444-4-44000000004-4-444-4-400000000000000000000000000000000000000000000000022−22−222200000000000000
χ6944-4-444-4-44000000004-4-444-4-4000000000000000000000000000000000000000000000000−222222−2200000000000000
χ7044-4-4-4-444-2004i4i−4i−4i00-22-222-2200−2i−2i2i2i000000000000−2i22i222−220000000000i2i2−i2−i2−2−22200000000000000000000000000
χ7144-4-4-4-444-2004i4i−4i−4i00-22-222-2200−2i−2i2i2i0000000000002i2−2i2−22220000000000−i2−i2i2i222−2−200000000000000000000000000
χ7244-4-4-4-444-200−4i−4i4i4i00-22-222-22002i2i−2i−2i000000000000−2i22i2−22220000000000i2i2−i2−i222−2−200000000000000000000000000
χ7344-4-4-4-444-200−4i−4i4i4i00-22-222-22002i2i−2i−2i0000000000002i2−2i222−220000000000−i2−i2i2i2−2−22200000000000000000000000000
χ744-44-44-4-444-440000-44-4-444-4-44000000-4-44400000000000000000000000000000000000000000000000000000000
χ754-44-44-4-44-24-400004-422-2-222-2000000-2-2220000004i−4i000000−2i−2i2i2i00000000000000000000000000000000000000
χ764-44-44-4-44-24-400004-422-2-222-2000000-2-222000000−4i4i0000002i2i−2i−2i00000000000000000000000000000000000000
χ774-44-44-4-44-2-440000-4422-2-222-200000022-2-2000000000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ784-44-44-4-44-2-440000-4422-2-222-200000022-2-20000000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ794-44-4-444-4-2444-44-4-4-42222-2-2-24-4-22-22-22-22000000000000-22000000000000000000000000000000000000000000
χ804-44-4-444-4-244-44-44-4-42222-2-2-2-442-22-2-22-220000000000002-2000000000000000000000000000000000000000000
χ814-4-444-44-44004i−4i−4i4i00-44-44-44-4004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ824-4-444-44-4400−4i4i4i−4i00-44-44-44-400−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ834-4-444-44-4-2004i−4i−4i4i002-22-22-2200−2i2i2i−2i000000000000000000000000006−6−66i6−i6−i6i600000000000000000000000000
χ844-4-444-44-4-2004i−4i−4i4i002-22-22-2200−2i2i2i−2i00000000000000000000000000−666−6−i6i6i6−i600000000000000000000000000
χ854-4-444-44-4-200−4i4i4i−4i002-22-22-22002i−2i−2i2i000000000000000000000000006−6−66−i6i6i6−i600000000000000000000000000
χ864-4-444-44-4-200−4i4i4i−4i002-22-22-22002i−2i−2i2i00000000000000000000000000−666−6i6−i6−i6i600000000000000000000000000
χ874-4-44-44-44400000000-444-44-4-40000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ884-4-44-44-44400000000-444-44-4-400000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ8988-8-888-8-8-400000000-444-4-444000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-88-88-4000000004-4-44-444000000000000000000000000000000000000000000000000000000000000000000

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