Finite Group Databasebeta

← Group #10868028

Character table — Group #10868028

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order122222223444444446666666441212121212121212444444448888121212121212121212122424242424242424444444448888888812121212244444
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
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ9111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-11111-1
χ10111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-11-1-1-1-11
χ11111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-11
χ12111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-11-1-1-11-1
χ13111111111-1-1-1-111111111111-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-11111-1-111-11-1-11-1
χ14111111111-1-1-1-111111111111-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1111-111-11
χ15111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-111-11-1-1-11
χ16111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111-1111-1
χ172222222222222-2-2-2-22222222-2-2-2-22222-2-2000000000000-2-2000000000000000022220000000000000000-2-20000
χ182222222222222-2-2-2-22222222-2-2-2-22222-2-2000000000000-2-20000000000000000-2-2-2-20000000000000000220000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000000022000000000000000022-2-200000000000000002-20000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000220000000000000000-2-2220000000000000000-220000
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
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-111111111111111110000000000000000-1-1-1-1000000
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
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-222-2-222-2-2111111-1-1-1-1-1-1-1-111110000000000000000-1-111000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-2-2-222-2-22211-1-1-1-111111111-1-1-1-10000000000000000-1-111000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-22222-2-2-2-222111111-1-1-1-11111-1-1-1-1000000000000000011-1-1000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-222-2-22222-2-211-1-1-1-11111-1-1-1-11111000000000000000011-1-1000000
χ2922-222-2-2-2222-2-20000-2-2-2-2222000022-2-200000000002−22−2000000000022−2−222−2−22i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i20000000000
χ3022-222-2-2-2222-2-20000-2-2-2-2222000022-2-200000000002−22−2000000000022−2−222−2−2−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i20000000000
χ3122-222-2-2-2222-2-20000-2-2-2-2222000022-2-20000000000−22−220000000000−2−222−2−2222i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i20000000000
χ3222-222-2-2-2222-2-20000-2-2-2-2222000022-2-20000000000−22−220000000000−2−222−2−222−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i20000000000
χ3322-222-2-2-22-2-2220000-2-2-2-22220000-2-22200000000002−2−22000000000022−2−2−2−2222i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i20000000000
χ3422-222-2-2-22-2-2220000-2-2-2-22220000-2-22200000000002−2−22000000000022−2−2−2−222−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i20000000000
χ3522-222-2-2-22-2-2220000-2-2-2-22220000-2-2220000000000−222−20000000000−2−22222−2−22i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i20000000000
χ3622-222-2-2-22-2-2220000-2-2-2-22220000-2-2220000000000−222−20000000000−2−22222−2−2−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i20000000000
χ3722-2-2-2-2222000022-2-2-2-222-22-2002-200002-20000002i−2i0000002i2i−2i−2i000000000000000022-2-22i−2i2i−2i00000000000000
χ3822-2-2-2-2222000022-2-2-2-222-22-2002-200002-20000002i−2i0000002i2i−2i−2i0000000000000000-2-222−2i2i−2i2i00000000000000
χ3922-2-2-2-2222000022-2-2-2-222-22-2002-200002-2000000−2i2i000000−2i−2i2i2i000000000000000022-2-2−2i2i−2i2i00000000000000
χ4022-2-2-2-2222000022-2-2-2-222-22-2002-200002-2000000−2i2i000000−2i−2i2i2i0000000000000000-2-2222i−2i2i−2i00000000000000
χ412-22-22-22-220000-22-222-22-22-2-200-2-200002200002i−2i0000000000002i2i−2i−2i0000000000002i−2i2i−2i00002-22-20000000000
χ422-22-22-22-220000-22-222-22-22-2-200-2-200002200002i−2i0000000000002i2i−2i−2i000000000000−2i2i−2i2i0000-22-220000000000
χ432-22-22-22-220000-22-222-22-22-2-200-2-20000220000−2i2i000000000000−2i−2i2i2i0000000000002i−2i2i−2i0000-22-220000000000
χ442-22-22-22-220000-22-222-22-22-2-200-2-20000220000−2i2i000000000000−2i−2i2i2i000000000000−2i2i−2i2i00002-22-20000000000
χ452-2-22-222-222i−2i2i−2i2-2-22-222-2-2-222i−2i2-22i−2i2i−2i-222i−2i2-2000000002i−2i000000000000000000000000000000002i−2i2-2000000
χ462-2-22-222-222i−2i2i−2i2-2-22-222-2-2-222i−2i2-22i−2i2i−2i-22−2i2i-22000000002i−2i00000000000000000000000000000000−2i2i-22000000
χ472-2-22-222-222i−2i2i−2i-222-2-222-2-2-22−2i2i-222i−2i2i−2i2-2000000000000−2i2i000000000000000000002i−2i−2i2i000000000000002-200
χ482-2-22-222-222i−2i2i−2i-222-2-222-2-2-22−2i2i-222i−2i2i−2i2-2000000000000−2i2i00000000000000000000−2i2i2i−2i00000000000000-2200
χ492-2-22-222-22−2i2i−2i2i2-2-22-222-2-2-22−2i2i2-2−2i2i−2i2i-222i−2i-2200000000−2i2i000000000000000000000000000000002i−2i-22000000
χ502-2-22-222-22−2i2i−2i2i2-2-22-222-2-2-22−2i2i2-2−2i2i−2i2i-22−2i2i2-200000000−2i2i00000000000000000000000000000000−2i2i2-2000000
χ512-2-22-222-22−2i2i−2i2i-222-2-222-2-2-222i−2i-22−2i2i−2i2i2-20000000000002i−2i000000000000000000002i−2i−2i2i00000000000000-2200
χ522-2-22-222-22−2i2i−2i2i-222-2-222-2-2-222i−2i-22−2i2i−2i2i2-20000000000002i−2i00000000000000000000−2i2i2i−2i000000000000002-200
χ532-2-22-222-2-12i−2i2i−2i2-2-221-1-1111-12i−2i-11−ii−ii1-12i−2i2-200000000−ii3−33−3−i3i3−i3i33−33−3−i3i3−i3i30000000000000000−ii-11000000
χ542-2-22-222-2-12i−2i2i−2i2-2-221-1-1111-12i−2i-11−ii−ii1-12i−2i2-200000000−ii−33−33i3−i3i3−i3−33−33i3−i3i3−i30000000000000000−ii-11000000
χ552-2-22-222-2-12i−2i2i−2i2-2-221-1-1111-12i−2i-11−ii−ii1-1−2i2i-2200000000−ii3−33−3−i3i3−i3i3−33−33i3−i3i3−i30000000000000000i−i1-1000000
χ562-2-22-222-2-12i−2i2i−2i2-2-221-1-1111-12i−2i-11−ii−ii1-1−2i2i-2200000000−ii−33−33i3−i3i3−i33−33−3−i3i3−i3i30000000000000000i−i1-1000000
χ572-2-22-222-2-1−2i2i−2i2i2-2-221-1-1111-1−2i2i-11i−ii−i1-12i−2i-2200000000i−i3−33−3i3−i3i3−i3−33−33−i3i3−i3i30000000000000000−ii1-1000000
χ582-2-22-222-2-1−2i2i−2i2i2-2-221-1-1111-1−2i2i-11i−ii−i1-12i−2i-2200000000i−i−33−33−i3i3−i3i33−33−3i3−i3i3−i30000000000000000−ii1-1000000
χ592-2-22-222-2-1−2i2i−2i2i2-2-221-1-1111-1−2i2i-11i−ii−i1-1−2i2i2-200000000i−i3−33−3i3−i3i3−i33−33−3i3−i3i3−i30000000000000000i−i-11000000
χ602-2-22-222-2-1−2i2i−2i2i2-2-221-1-1111-1−2i2i-11i−ii−i1-1−2i2i2-200000000i−i−33−33−i3i3−i3i3−33−33−i3i3−i3i30000000000000000i−i-11000000
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200000000000022000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000000000
χ63444-4-44-4-440000000044-4-4-44-400000000000000000000000000000000000000000000000022−22−222200000000000000
χ64444-4-44-4-440000000044-4-4-44-4000000000000000000000000000000000000000000000000−222222−2200000000000000
χ6544-444-4-4-4-244-4-400002222-2-2-20000-2-222000000000022−2222−220000000000−2−222−2−22200000000000000000000000000
χ6644-444-4-4-4-244-4-400002222-2-2-20000-2-2220000000000−2222−2222000000000022−2−222−2−200000000000000000000000000
χ6744-444-4-4-4-2-4-44400002222-2-2-2000022-2-2000000000022−22−22220000000000−2−22222−2−200000000000000000000000000
χ6844-444-4-4-4-2-4-44400002222-2-2-2000022-2-20000000000−222222−22000000000022−2−2−2−22200000000000000000000000000
χ6944-4-4-4-44440000-4-444-4-444-44-400-440000-4400000000000000000000000000000000000000000000000000000000
χ7044-4-4-4-444-2000044-4-422-2-22-2200-220000-220000004i−4i000000−2i−2i2i2i00000000000000000000000000000000000000
χ7144-4-4-4-444-2000044-4-422-2-22-2200-220000-22000000−4i4i0000002i2i−2i−2i00000000000000000000000000000000000000
χ7244-4-4-4-444-20000-4-44422-2-22-22002-200002-200000000000000000023−23−23230000000000000000000000000000000000
χ7344-4-4-4-444-20000-4-44422-2-22-22002-200002-2000000000000000000−232323−230000000000000000000000000000000000
χ744-444-4-4-4444i−4i−4i4i00004-4-44-4-4400004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ754-444-4-4-444−4i4i4i−4i00004-4-44-4-440000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ764-444-4-4-44-24i−4i−4i4i0000-222-222-20000−2i2i2i−2i0000000000000000000000006−6−66−i6i6i6−i600000000000000000000000000
χ774-444-4-4-44-24i−4i−4i4i0000-222-222-20000−2i2i2i−2i000000000000000000000000−666−6i6−i6−i6i600000000000000000000000000
χ784-444-4-4-44-2−4i4i4i−4i0000-222-222-200002i−2i−2i2i0000000000000000000000006−6−66i6−i6−i6i600000000000000000000000000
χ794-444-4-4-44-2−4i4i4i−4i0000-222-222-200002i−2i−2i2i000000000000000000000000−666−6−i6i6i6−i600000000000000000000000000
χ804-44-44-44-4400004-44-44-44-44-4-400440000-4-400000000000000000000000000000000000000000000000000000000
χ814-44-44-44-4-200004-44-4-22-22-22200-2-200002200000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ824-44-44-44-4-200004-44-4-22-22-22200-2-2000022000000000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ834-44-44-44-4-20000-44-44-22-22-22200220000-2-200004i−4i000000000000−2i−2i2i2i0000000000000000000000000000000000
χ844-44-44-44-4-20000-44-44-22-22-22200220000-2-20000−4i4i0000000000002i2i−2i−2i0000000000000000000000000000000000
χ854-4-44-444-4-24i−4i4i−4i-444-42-2-2222-2−4i4i2-2−2i2i−2i2i-220000000000002i−2i000000000000000000000000000000000000000000
χ864-4-44-444-4-2−4i4i−4i4i-444-42-2-2222-24i−4i2-22i−2i2i−2i-22000000000000−2i2i000000000000000000000000000000000000000000
χ874-4-4-444-44400000000-44-444-4-40000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ884-4-4-444-44400000000-44-444-4-400000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ89888-8-88-8-8-400000000-4-4444-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-888-88-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000000000

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