Finite Group Databasebeta

← Group #10855223

Character table — Group #10855223

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order12222222344444444666666644121212121212121222444444666688881212121212122424242424242424222244448888888812121212444424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ51111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ61111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-11-1-11-1-1
χ91111111111-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111111-1-11-1-1-1-11
χ101111111111-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-11111-1
χ111111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-111-1-1-111-1
χ121111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111111-1-11
χ131111111111-1-1-1-11111111111-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111111111-1-11111-1-1-1-111-1-11-1-1-11-1
χ141111111111-1-1-1-11111111111-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1111-11
χ151111111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-11-11
χ161111111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111-11-1
χ17222222222-22222-2-2-22222222-2-2-2-22222-2-20000000000000000-2-200000000000000002222000000000000-200-200
χ18222222222-22222-2-2-22222222-2-2-2-22222-2-20000000000000000-2-20000000000000000-2-2-2-2000000000000200200
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000000022000000000000000022-2-2000000000000-200200
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000000000000220000000000000000-2-222000000000000200-200
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-2-2-2-2-1-1-1-1-1-11111111100000000000000001111000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-22222-2-21111-2-2-2-2-1-11111111111110000000000000000-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-100000000000000001111000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-12222-2-2-2-2-1-1-1-122-2-2111111-1-1-1-111110000000000000000-1-111000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-222-2-2-1-1-1-1-2-2221111111111-1-1-1-1000000000000000011-1-1000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-222-2-2221111-2-22211-1-1-1-11111-1-1-1-10000000000000000-1-111000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-2-2-22222111122-2-211-1-1-1-1-1-1-1-11111000000000000000011-1-1000000
χ29222-2-22-2-22-200002-2222-22-2-2-200-2-20000220000002i−2i00000000002i2i−2i−2i0000000022-2-200002i2i−2i−2i00000000000000
χ30222-2-22-2-22-200002-2222-22-2-2-200-2-20000220000002i−2i00000000002i2i−2i−2i00000000-2-2220000−2i−2i2i2i00000000000000
χ31222-2-22-2-22-200002-2222-22-2-2-200-2-2000022000000−2i2i0000000000−2i−2i2i2i0000000022-2-20000−2i−2i2i2i00000000000000
χ32222-2-22-2-22-200002-2222-22-2-2-200-2-2000022000000−2i2i0000000000−2i−2i2i2i00000000-2-22200002i2i−2i−2i00000000000000
χ3322-22-2-22-2202i2i−2i−2i0002-22-2-22-200002i2i−2i−2i00000000000000−i2i22−2000000−i2−i2i2i222−2−200002i−2i2-2−i2i2−i2i222−2−20000000000
χ3422-22-2-22-2202i2i−2i−2i0002-22-2-22-200002i2i−2i−2i00000000000000−i2i22−2000000−i2−i2i2i222−2−20000−2i2i-22i2−i2i2−i2−2−2220000000000
χ3522-22-2-22-2202i2i−2i−2i0002-22-2-22-200002i2i−2i−2i00000000000000i2−i2−22000000i2i2−i2−i2−2−22200002i−2i2-2i2−i2i2−i2−2−2220000000000
χ3622-22-2-22-2202i2i−2i−2i0002-22-2-22-200002i2i−2i−2i00000000000000i2−i2−22000000i2i2−i2−i2−2−2220000−2i2i-22−i2i2−i2i222−2−20000000000
χ3722-22-2-22-220−2i−2i2i2i0002-22-2-22-20000−2i−2i2i2i00000000000000−i2i2−22000000−i2−i2i2i2−2−22200002i−2i-22i2−i2i2−i222−2−20000000000
χ3822-22-2-22-220−2i−2i2i2i0002-22-2-22-20000−2i−2i2i2i00000000000000−i2i2−22000000−i2−i2i2i2−2−2220000−2i2i2-2−i2i2−i2i2−2−2220000000000
χ3922-22-2-22-220−2i−2i2i2i0002-22-2-22-20000−2i−2i2i2i00000000000000i2−i22−2000000i2i2−i2−i222−2−200002i−2i-22−i2i2−i2i2−2−2220000000000
χ4022-22-2-22-220−2i−2i2i2i0002-22-2-22-20000−2i−2i2i2i00000000000000i2−i22−2000000i2i2−i2−i222−2−20000−2i2i2-2i2−i2i2−i222−2−20000000000
χ412-2222-2-2-2222i−2i2i−2i-2-22-2-2222-2-22i−2i2-22i−2i2i−2i2-200000000000000002i−2i0000000000002-22-2000000000000000002i−2i000
χ422-2222-2-2-2222i−2i2i−2i-2-22-2-2222-2-22i−2i2-22i−2i2i−2i2-200000000000000002i−2i000000000000-22-2200000000000000000−2i2i000
χ432-2222-2-2-222−2i2i−2i2i-2-22-2-2222-2-2−2i2i2-2−2i2i−2i2i2-20000000000000000−2i2i0000000000002-22-200000000000000000−2i2i000
χ442-2222-2-2-222−2i2i−2i2i-2-22-2-2222-2-2−2i2i2-2−2i2i−2i2i2-20000000000000000−2i2i000000000000-22-22000000000000000002i−2i000
χ452-2222-2-2-22-22i−2i2i−2i22-2-2-2222-2-2−2i2i-222i−2i2i−2i-22002-22i−2i0000000000−2i2i00000000000000000000000000002-22i−2i000000
χ462-2222-2-2-22-22i−2i2i−2i22-2-2-2222-2-2−2i2i-222i−2i2i−2i-2200-22−2i2i0000000000−2i2i0000000000000000000000000000-22−2i2i000000
χ472-2222-2-2-22-2−2i2i−2i2i22-2-2-2222-2-22i−2i-22−2i2i−2i2i-22002-2−2i2i00000000002i−2i00000000000000000000000000002-2−2i2i000000
χ482-2222-2-2-22-2−2i2i−2i2i22-2-2-2222-2-22i−2i-22−2i2i−2i2i-2200-222i−2i00000000002i−2i0000000000000000000000000000-222i−2i000000
χ492-2222-2-2-2-1-22i−2i2i−2i22-211-1-1-111−2i2i1-1−ii−ii1-1002-22i−2i00−i3−i3i3i30000i−i3−33−3−i3i3−i3i33−33−30000000000000000-11−ii000000
χ502-2222-2-2-2-1-22i−2i2i−2i22-211-1-1-111−2i2i1-1−ii−ii1-1002-22i−2i00i3i3−i3−i30000i−i−33−33i3−i3i3−i3−33−330000000000000000-11−ii000000
χ512-2222-2-2-2-1-22i−2i2i−2i22-211-1-1-111−2i2i1-1−ii−ii1-100-22−2i2i00−i3−i3i3i30000i−i3−33−3i3−i3i3−i3−33−3300000000000000001-1i−i000000
χ522-2222-2-2-2-1-22i−2i2i−2i22-211-1-1-111−2i2i1-1−ii−ii1-100-22−2i2i00i3i3−i3−i30000i−i−33−33−i3i3−i3i33−33−300000000000000001-1i−i000000
χ532-2222-2-2-2-1-2−2i2i−2i2i22-211-1-1-1112i−2i1-1i−ii−i1-1002-2−2i2i00−i3−i3i3i30000−ii−33−33−i3i3−i3i3−33−330000000000000000-11i−i000000
χ542-2222-2-2-2-1-2−2i2i−2i2i22-211-1-1-1112i−2i1-1i−ii−i1-1002-2−2i2i00i3i3−i3−i30000−ii3−33−3i3−i3i3−i33−33−30000000000000000-11i−i000000
χ552-2222-2-2-2-1-2−2i2i−2i2i22-211-1-1-1112i−2i1-1i−ii−i1-100-222i−2i00−i3−i3i3i30000−ii−33−33i3−i3i3−i33−33−300000000000000001-1−ii000000
χ562-2222-2-2-2-1-2−2i2i−2i2i22-211-1-1-1112i−2i1-1i−ii−i1-100-222i−2i00i3i3−i3−i30000−ii3−33−3−i3i3−i3i3−33−3300000000000000001-1−ii000000
χ572-22-2-2-2222-20000-222-2-2-22-22200-2200002-22-20000002-22-20000000000000000002-2-22000000002-22-20000000000
χ582-22-2-2-2222-20000-222-2-2-22-22200-2200002-22-20000002-22-2000000000000000000-222-200000000-22-220000000000
χ592-22-2-2-2222-20000-222-2-2-22-22200-2200002-2-22000000-22-220000000000000000002-2-2200000000-22-220000000000
χ602-22-2-2-2222-20000-222-2-2-22-22200-2200002-2-22000000-22-22000000000000000000-222-2000000002-22-20000000000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200000000000000002200000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000000000000000-2-200000000000000000000000000000000000000
χ63444-4-44-4-4440000-44-444-44-4-4-400440000-4-400000000000000000000000000000000000000000000000000000000
χ64444-4-44-4-4-240000-44-4-2-22-222200-2-200002200000000−2i32i32i3−2i300000000000000000000000000000000000000000000
χ65444-4-44-4-4-240000-44-4-2-22-222200-2-2000022000000002i3−2i3−2i32i300000000000000000000000000000000000000000000
χ66444-4-44-4-4-2-400004-44-2-22-222200220000-2-20000004i−4i0000000000−2i−2i2i2i0000000000000000000000000000000000
χ67444-4-44-4-4-2-400004-44-2-22-222200220000-2-2000000−4i4i00000000002i2i−2i−2i0000000000000000000000000000000000
χ6844-44-4-44-4-204i4i−4i−4i000-22-222-220000−2i−2i2i2i00000000000000−2i22i222−22000000i2i2−i2−i2−2−22200000000000000000000000000
χ6944-44-4-44-4-204i4i−4i−4i000-22-222-220000−2i−2i2i2i000000000000002i2−2i2−2222000000−i2−i2i2i222−2−200000000000000000000000000
χ7044-44-4-44-4-20−4i−4i4i4i000-22-222-2200002i2i−2i−2i00000000000000−2i22i2−2222000000i2i2−i2−i222−2−200000000000000000000000000
χ7144-44-4-44-4-20−4i−4i4i4i000-22-222-2200002i2i−2i−2i000000000000002i2−2i222−22000000−i2−i2i2i2−2−22200000000000000000000000000
χ7244-4-44-4-444000000004-4-4-44-4400000000000000000000000000000000000000000000000022−22−222200000000000000
χ7344-4-44-4-444000000004-4-4-44-44000000000000000000000000000000000000000000000000−222222−2200000000000000
χ744-4444-4-4-4-244i−4i4i−4i-4-4422-2-2-2224i−4i-22−2i2i−2i2i-220000000000000000−2i2i00000000000000000000000000000000000000
χ754-4444-4-4-4-24−4i4i−4i4i-4-4422-2-2-222−4i4i-222i−2i2i−2i-2200000000000000002i−2i00000000000000000000000000000000000000
χ764-44-4-4-4444400004-4-4-4-4-44-444004-40000-4400000000000000000000000000000000000000000000000000000000
χ774-44-4-4-444-2400004-4-4222-22-2-200-2200002-2000000000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ784-44-4-4-444-2400004-4-4222-22-2-200-2200002-20000000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ794-44-4-4-444-2-40000-444222-22-2-2002-20000-224-4000000-22-2200000000000000000000000000000000000000000000
χ804-44-4-4-444-2-40000-444222-22-2-2002-20000-22-440000002-22-200000000000000000000000000000000000000000000
χ814-4-44-44-44404-4-44000-444-4-4-4400004-4-440000000000000000000000000000000000000000000000000000000000
χ824-4-44-44-4440-444-4000-444-4-4-440000-444-40000000000000000000000000000000000000000000000000000000000
χ834-4-44-44-44-204-4-440002-2-2222-20000-222-20000000000000000000000006−6−666−6−6600000000000000000000000000
χ844-4-44-44-44-204-4-440002-2-2222-20000-222-2000000000000000000000000−666−6−666−600000000000000000000000000
χ854-4-44-44-44-20-444-40002-2-2222-200002-2-220000000000000000000000006−6−66−666−600000000000000000000000000
χ864-4-44-44-44-20-444-40002-2-2222-200002-2-22000000000000000000000000−666−66−6−6600000000000000000000000000
χ874-4-4-4444-4400000000-44-4-444-4000000000000000000000000000000000000000000000000000022−22−22220000000000
χ884-4-4-4444-4400000000-44-4-444-40000000000000000000000000000000000000000000000000000−222222−220000000000
χ8988-8-88-8-88-400000000-4444-44-4000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-8888-8-4000000004-444-4-44000000000000000000000000000000000000000000000000000000000000000000

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