Finite Group Databasebeta

← Group #10868448

Character table — Group #10868448

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order122222223444444446666666441212121212121212444444448888121212121212121212122424242424242424444444448888888812121212224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ91111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11-1-11
χ101111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-111-1
χ111111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111111-1-11
χ121111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-111-1-1-111-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111111111-1-1-1-111-1-1-1-11-11-1
χ141111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-111-11-11
χ151111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111-11-1
χ161111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-11-11
χ17222222222-22222-2-2-22222222-2-22222-2-2-2-2000000000000-2-200000000000000002222000000000000000000-2-200
χ18222222222-22222-2-2-22222222-2-22222-2-2-2-2000000000000-2-20000000000000000-2-2-2-20000000000000000002200
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000000022000000000000000022-2-2000000000000000000-2200
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000220000000000000000-2-2220000000000000000002-200
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
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000000000001111000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111111111110000000000000000-1-1-1-1000000
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
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-222-2-222-2-211-1-1-1-11111-1-1-1-111110000000000000000-1-111000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-2-2-222-2-22211-1-1-1-111111111-1-1-1-1000000000000000011-1-1000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-22222-2-2-2-222111111-1-1-1-11111-1-1-1-10000000000000000-1-111000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-222-2-22222-2-2111111-1-1-1-1-1-1-1-11111000000000000000011-1-1000000
χ2922-2-22-2-222022-2-2000-22-222-2-20022-2-2000000000000−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i22i−2i2i−2i000022−2−222−2−20000000000
χ3022-2-22-2-222022-2-2000-22-222-2-20022-2-2000000000000−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i0000−2−222−2−2220000000000
χ3122-2-22-2-222022-2-2000-22-222-2-20022-2-2000000000000i2−i2i2−i20000000000i2i2−i2−i2i2i2−i2−i22i−2i2i−2i0000−2−222−2−2220000000000
χ3222-2-22-2-222022-2-2000-22-222-2-20022-2-2000000000000i2−i2i2−i20000000000i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i000022−2−222−2−20000000000
χ3322-2-22-2-2220-2-222000-22-222-2-200-2-222000000000000−i2i2i2−i20000000000−i2−i2i2i2i2i2−i2−i22i−2i−2i2i0000−2−22222−2−20000000000
χ3422-2-22-2-2220-2-222000-22-222-2-200-2-222000000000000−i2i2i2−i20000000000−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i000022−2−2−2−2220000000000
χ3522-2-22-2-2220-2-222000-22-222-2-200-2-222000000000000i2−i2−i2i20000000000i2i2−i2−i2−i2−i2i2i22i−2i−2i2i000022−2−2−2−2220000000000
χ3622-2-22-2-2220-2-222000-22-222-2-200-2-222000000000000i2−i2−i2i20000000000i2i2−i2−i2−i2−i2i2i2−2i2i2i−2i0000−2−22222−2−20000000000
χ3722-2-2-222-2220000-22-2-2-2-22-22200000022-2-2002i−2i000000000000002i2i−2i−2i0000000000002i2i−2i−2i2-22-200000000000000
χ3822-2-2-222-2220000-22-2-2-2-22-22200000022-2-2002i−2i000000000000002i2i−2i−2i000000000000−2i−2i2i2i-22-2200000000000000
χ3922-2-2-222-2220000-22-2-2-2-22-22200000022-2-200−2i2i00000000000000−2i−2i2i2i0000000000002i2i−2i−2i-22-2200000000000000
χ4022-2-2-222-2220000-22-2-2-2-22-22200000022-2-200−2i2i00000000000000−2i−2i2i2i000000000000−2i−2i2i2i2-22-200000000000000
χ412-22-22-22-2222i−2i2i−2i-2-222-2-2-22-222i−2i2i−2i2i−2i2-22-20000000000002i−2i000000000000000000002i−2i2i−2i0000000000002-20000
χ422-22-22-22-2222i−2i2i−2i-2-222-2-2-22-222i−2i2i−2i2i−2i2-22-20000000000002i−2i00000000000000000000−2i2i−2i2i000000000000-220000
χ432-22-22-22-222−2i2i−2i2i-2-222-2-2-22-22−2i2i−2i2i−2i2i2-22-2000000000000−2i2i000000000000000000002i−2i2i−2i000000000000-220000
χ442-22-22-22-222−2i2i−2i2i-2-222-2-2-22-22−2i2i−2i2i−2i2i2-22-2000000000000−2i2i00000000000000000000−2i2i−2i2i0000000000002-20000
χ452-22-22-22-22-22i−2i2i−2i22-22-2-2-22-22−2i2i2i−2i2i−2i-22-2200002i−2i2-20000−2i2i000000000000000000000000000000002i−2i2-2000000
χ462-22-22-22-22-22i−2i2i−2i22-22-2-2-22-22−2i2i2i−2i2i−2i-22-220000−2i2i-220000−2i2i00000000000000000000000000000000−2i2i-22000000
χ472-22-22-22-22-2−2i2i−2i2i22-22-2-2-22-222i−2i−2i2i−2i2i-22-2200002i−2i-2200002i−2i000000000000000000000000000000002i−2i-22000000
χ482-22-22-22-22-2−2i2i−2i2i22-22-2-2-22-222i−2i−2i2i−2i2i-22-220000−2i2i2-200002i−2i00000000000000000000000000000000−2i2i2-2000000
χ492-22-22-22-2-1-22i−2i2i−2i22-2-1111-11-1−2i2i−ii−ii1-11-100002i−2i2-20000i−i33−3−3−i3i3−i3i3−i3i3−i3i33−33−30000000000000000−ii-11000000
χ502-22-22-22-2-1-22i−2i2i−2i22-2-1111-11-1−2i2i−ii−ii1-11-100002i−2i2-20000i−i−3−333i3−i3i3−i3i3−i3i3−i3−33−330000000000000000−ii-11000000
χ512-22-22-22-2-1-22i−2i2i−2i22-2-1111-11-1−2i2i−ii−ii1-11-10000−2i2i-220000i−i33−3−3−i3i3−i3i3i3−i3i3−i3−33−330000000000000000i−i1-1000000
χ522-22-22-22-2-1-22i−2i2i−2i22-2-1111-11-1−2i2i−ii−ii1-11-10000−2i2i-220000i−i−3−333i3−i3i3−i3−i3i3−i3i33−33−30000000000000000i−i1-1000000
χ532-22-22-22-2-1-2−2i2i−2i2i22-2-1111-11-12i−2ii−ii−i1-11-100002i−2i-220000−ii33−3−3i3−i3i3−i3−i3i3−i3i3−33−330000000000000000−ii1-1000000
χ542-22-22-22-2-1-2−2i2i−2i2i22-2-1111-11-12i−2ii−ii−i1-11-100002i−2i-220000−ii−3−333−i3i3−i3i3i3−i3i3−i33−33−30000000000000000−ii1-1000000
χ552-22-22-22-2-1-2−2i2i−2i2i22-2-1111-11-12i−2ii−ii−i1-11-10000−2i2i2-20000−ii33−3−3i3−i3i3−i3i3−i3i3−i33−33−30000000000000000i−i-11000000
χ562-22-22-22-2-1-2−2i2i−2i2i22-2-1111-11-12i−2ii−ii−i1-11-10000−2i2i2-20000−ii−3−333−i3i3−i3i3−i3i3−i3i3−33−330000000000000000i−i-11000000
χ572-2-22-2-2222200002-2-2-222-2-2-220000002-2-222i−2i0000000000002i−2i2i−2i00000000000000002-2-2200002i−2i2i−2i0000000000
χ582-2-22-2-2222200002-2-2-222-2-2-220000002-2-222i−2i0000000000002i−2i2i−2i0000000000000000-222-20000−2i2i−2i2i0000000000
χ592-2-22-2-2222200002-2-2-222-2-2-220000002-2-22−2i2i000000000000−2i2i−2i2i00000000000000002-2-220000−2i2i−2i2i0000000000
χ602-2-22-2-2222200002-2-2-222-2-2-220000002-2-22−2i2i000000000000−2i2i−2i2i0000000000000000-222-200002i−2i2i−2i0000000000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000000022000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000000000
χ634444-4-4-4-44000000004-444-4-4-400000000000000000000000000000000000000000000000022−22−222200000000000000
χ644444-4-4-4-44000000004-444-4-4-4000000000000000000000000000000000000000000000000−222222−2200000000000000
χ6544-4-44-4-44-2044-4-40002-22-2-22200-2-222000000000000−2i22i2−2i22i20000000000i2i2−i2−i2i2i2−i2−i200000000000000000000000000
χ6644-4-44-4-44-2044-4-40002-22-2-22200-2-2220000000000002i2−2i22i2−2i20000000000−i2−i2i2i2−i2−i2i2i200000000000000000000000000
χ6744-4-44-4-44-20-4-4440002-22-2-2220022-2-2000000000000−2i22i22i2−2i20000000000i2i2−i2−i2−i2−i2i2i200000000000000000000000000
χ6844-4-44-4-44-20-4-4440002-22-2-2220022-2-20000000000002i2−2i2−2i22i20000000000−i2−i2i2i2i2i2−i2−i200000000000000000000000000
χ6944-4-4-444-44-400004-44-4-4-44-444000000-4-44400000000000000000000000000000000000000000000000000000000
χ7044-4-4-444-4-240000-44-4222-22-2-2000000-2-222004i−4i00000000000000−2i−2i2i2i0000000000000000000000000000000000
χ7144-4-4-444-4-240000-44-4222-22-2-2000000-2-22200−4i4i000000000000002i2i−2i−2i0000000000000000000000000000000000
χ7244-4-4-444-4-2-400004-44222-22-2-200000022-2-200000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ7344-4-4-444-4-2-400004-44222-22-2-200000022-2-2000000000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ744-44-44-44-4-244i−4i4i−4i-4-44-2222-22-24i−4i−2i2i−2i2i-22-22000000000000−2i2i000000000000000000000000000000000000000000
χ754-44-44-44-4-24−4i4i−4i4i-4-44-2222-22-2−4i4i2i−2i2i−2i-22-220000000000002i−2i000000000000000000000000000000000000000000
χ764-44-4-44-4440000000044-4-4-44-40000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ774-44-4-44-4440000000044-4-4-44-400000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ784-4-4444-4-4404i−4i−4i4i000-4-44-444-4004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-4-440−4i4i4i−4i000-4-44-444-400−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ804-4-4444-4-4-204i−4i−4i4i00022-22-2-2200−2i2i2i−2i000000000000000000000000006−6−66i6−i6−i6i600000000000000000000000000
χ814-4-4444-4-4-204i−4i−4i4i00022-22-2-2200−2i2i2i−2i00000000000000000000000000−666−6−i6i6i6−i600000000000000000000000000
χ824-4-4444-4-4-20−4i4i4i−4i00022-22-2-22002i−2i−2i2i000000000000000000000000006−6−66−i6i6i6−i600000000000000000000000000
χ834-4-4444-4-4-20−4i4i4i−4i00022-22-2-22002i−2i−2i2i00000000000000000000000000−666−6i6−i6−i6i600000000000000000000000000
χ844-4-44-4-4444-40000-444-444-4-4-44000000-444-400000000000000000000000000000000000000000000000000000000
χ854-4-44-4-444-2400004-4-42-2-2222-2000000-222-24i−4i000000000000−2i2i−2i2i00000000000000000000000000000000000000
χ864-4-44-4-444-2400004-4-42-2-2222-2000000-222-2−4i4i0000000000002i−2i2i−2i00000000000000000000000000000000000000
χ874-4-44-4-444-2-40000-4442-2-2222-20000002-2-2200000000000000000023−23−23230000000000000000000000000000000000
χ884-4-44-4-444-2-40000-4442-2-2222-20000002-2-22000000000000000000−232323−230000000000000000000000000000000000
χ898888-8-8-8-8-400000000-44-4-4444000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-88-400000000-4-4444-44000000000000000000000000000000000000000000000000000000000000000000

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