Finite Group Databasebeta

← Group #10868013

Character table — Group #10868013

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order122222223444444446666666441212121212121212444444448888121212121212121212122424242424242424444444448888888812121212222444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ4111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1
χ51111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ61111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-11-1-11-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ91111111111-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-111-1-11-1-1-1-11
χ101111111111-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-11111-1
χ111111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111111-1-11
χ121111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-111-1-1-111-1
χ131111111111-1-1-1-11111111111-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1111111-1-11-1-1-11-1
χ141111111111-1-1-1-11111111111-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1111-11
χ151111111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111-11-1
χ161111111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-11-11
χ17222222222-22222-2-2-22222222-2-2-2-22222-2-20000000000000000-2-200000000000022220000000000000000-200-200
χ18222222222-22222-2-2-22222222-2-2-2-22222-2-20000000000000000-2-2000000000000-2-2-2-20000000000000000200200
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000000000002200000000000022-2-20000000000000000-200200
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000000022000000000000-2-2220000000000000000200-200
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
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000000000001111000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-21111-1-11111111111110000000000000000-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111-1-11111-1-1-1-1-1-1-1-100000000000000001111000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-12222-2-2-2-2-2-222-1-1-1-1111111-1-1-1-111110000000000000000-1-111000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-2-2-22222-2-2-1-1-1-11111111111-1-1-1-1000000000000000011-1-1000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-22222-2-222-2-2111111-1-1-1-11111-1-1-1-10000000000000000-1-111000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-2-2-22222-2-222111111-1-1-1-1-1-1-1-11111000000000000000011-1-1000000
χ2922-22-2-2-22222i2i−2i−2i-2-222-22-2-2-222i−2i2-22i2i−2i−2i2-2002i−2i002-2000000002i−2i00000000000000000000000000002i−2i2-2000000
χ3022-22-2-2-22222i2i−2i−2i-2-222-22-2-2-222i−2i2-22i2i−2i−2i2-200−2i2i00-22000000002i−2i0000000000000000000000000000−2i2i-22000000
χ3122-22-2-2-2222−2i−2i2i2i-2-222-22-2-2-22−2i2i2-2−2i−2i2i2i2-2002i−2i00-2200000000−2i2i00000000000000000000000000002i−2i-22000000
χ3222-22-2-2-2222−2i−2i2i2i-2-222-22-2-2-22−2i2i2-2−2i−2i2i2i2-200−2i2i002-200000000−2i2i0000000000000000000000000000−2i2i2-2000000
χ3322-22-2-2-222-22i2i−2i−2i22-22-22-2-2-22−2i2i-222i2i−2i−2i-220000000000000000−2i2i00000000000000002i2i−2i−2i00000000000002-2000
χ3422-22-2-2-222-22i2i−2i−2i22-22-22-2-2-22−2i2i-222i2i−2i−2i-220000000000000000−2i2i0000000000000000−2i−2i2i2i0000000000000-22000
χ3522-22-2-2-222-2−2i−2i2i2i22-22-22-2-2-222i−2i-22−2i−2i2i2i-2200000000000000002i−2i00000000000000002i2i−2i−2i0000000000000-22000
χ3622-22-2-2-222-2−2i−2i2i2i22-22-22-2-2-222i−2i-22−2i−2i2i2i-2200000000000000002i−2i0000000000000000−2i−2i2i2i00000000000002-2000
χ3722-22-2-2-22-122i2i−2i−2i-2-22-11-1111-12i−2i-11−i−iii-11002i−2i002-2000033−3−3−ii−i3−i3i3i3−i3−i3i3i333−3−30000000000000000−ii-11000000
χ3822-22-2-2-22-122i2i−2i−2i-2-22-11-1111-12i−2i-11−i−iii-11002i−2i002-20000−3−333−iii3i3−i3−i3i3i3−i3−i3−3−3330000000000000000−ii-11000000
χ3922-22-2-2-22-122i2i−2i−2i-2-22-11-1111-12i−2i-11−i−iii-1100−2i2i00-22000033−3−3−ii−i3−i3i3i3i3i3−i3−i3−3−3330000000000000000i−i1-1000000
χ4022-22-2-2-22-122i2i−2i−2i-2-22-11-1111-12i−2i-11−i−iii-1100−2i2i00-220000−3−333−iii3i3−i3−i3−i3−i3i3i333−3−30000000000000000i−i1-1000000
χ4122-22-2-2-22-12−2i−2i2i2i-2-22-11-1111-1−2i2i-11ii−i−i-11002i−2i00-22000033−3−3i−ii3i3−i3−i3−i3−i3i3i3−3−3330000000000000000−ii1-1000000
χ4222-22-2-2-22-12−2i−2i2i2i-2-22-11-1111-1−2i2i-11ii−i−i-11002i−2i00-220000−3−333i−i−i3−i3i3i3i3i3−i3−i333−3−30000000000000000−ii1-1000000
χ4322-22-2-2-22-12−2i−2i2i2i-2-22-11-1111-1−2i2i-11ii−i−i-1100−2i2i002-2000033−3−3i−ii3i3−i3−i3i3i3−i3−i333−3−30000000000000000i−i-11000000
χ4422-22-2-2-22-12−2i−2i2i2i-2-22-11-1111-1−2i2i-11ii−i−i-1100−2i2i002-20000−3−333i−i−i3−i3i3i3−i3−i3i3i3−3−3330000000000000000i−i-11000000
χ4522-2-22-22-2202i−2i2i−2i0002-2-2-222-200002i−2i2i−2i0000000000−i2i22−200000000002−22−2−i2i2−i2i22i−2i2-20000−i2−i2i2i222−2−20000000000
χ4622-2-22-22-2202i−2i2i−2i0002-2-2-222-200002i−2i2i−2i0000000000−i2i22−200000000002−22−2−i2i2−i2i2−2i2i-220000i2i2−i2−i2−2−2220000000000
χ4722-2-22-22-2202i−2i2i−2i0002-2-2-222-200002i−2i2i−2i0000000000i2−i2−220000000000−22−22i2−i2i2−i22i−2i2-20000i2i2−i2−i2−2−2220000000000
χ4822-2-22-22-2202i−2i2i−2i0002-2-2-222-200002i−2i2i−2i0000000000i2−i2−220000000000−22−22i2−i2i2−i2−2i2i-220000−i2−i2i2i222−2−20000000000
χ4922-2-22-22-220−2i2i−2i2i0002-2-2-222-20000−2i2i−2i2i0000000000−i2i2−220000000000−22−22−i2i2−i2i22i−2i-220000i2i2−i2−i222−2−20000000000
χ5022-2-22-22-220−2i2i−2i2i0002-2-2-222-20000−2i2i−2i2i0000000000−i2i2−220000000000−22−22−i2i2−i2i2−2i2i2-20000−i2−i2i2i2−2−2220000000000
χ5122-2-22-22-220−2i2i−2i2i0002-2-2-222-20000−2i2i−2i2i0000000000i2−i22−200000000002−22−2i2−i2i2−i22i−2i-220000−i2−i2i2i2−2−2220000000000
χ5222-2-22-22-220−2i2i−2i2i0002-2-2-222-20000−2i2i−2i2i0000000000i2−i22−200000000002−22−2i2−i2i2−i2−2i2i2-20000i2i2−i2−i222−2−20000000000
χ532-2222-2-2-22-200002-22-222-22-2-200-2-200002200002i−2i0000000000002i−2i2i−2i0000000000002i−2i2i−2i00002-22-20000000000
χ542-2222-2-2-22-200002-22-222-22-2-200-2-200002200002i−2i0000000000002i−2i2i−2i000000000000−2i2i−2i2i0000-22-220000000000
χ552-2222-2-2-22-200002-22-222-22-2-200-2-20000220000−2i2i000000000000−2i2i−2i2i0000000000002i−2i2i−2i0000-22-220000000000
χ562-2222-2-2-22-200002-22-222-22-2-200-2-20000220000−2i2i000000000000−2i2i−2i2i000000000000−2i2i−2i2i00002-22-20000000000
χ572-2-22-222-22200002-2-2-2-222-22-2002-20000-222i−2i00000000002i−2i2i−2i0000000000000000002-2-222i−2i2i−2i00000000000000
χ582-2-22-222-22200002-2-2-2-222-22-2002-20000-222i−2i00000000002i−2i2i−2i000000000000000000-222-2−2i2i−2i2i00000000000000
χ592-2-22-222-22200002-2-2-2-222-22-2002-20000-22−2i2i0000000000−2i2i−2i2i0000000000000000002-2-22−2i2i−2i2i00000000000000
χ602-2-22-222-22200002-2-2-2-222-22-2002-20000-22−2i2i0000000000−2i2i−2i2i000000000000000000-222-22i−2i2i−2i00000000000000
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
χ63444-4-44-4-4404-4-4400044-44-4-4-400004-4-440000000000000000000000000000000000000000000000000000000000
χ64444-4-44-4-440-444-400044-44-4-4-40000-444-40000000000000000000000000000000000000000000000000000000000
χ65444-4-44-4-4-204-4-44000-2-22-22220000-222-2000000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ66444-4-44-4-4-204-4-44000-2-22-22220000-222-2000000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ67444-4-44-4-4-20-444-4000-2-22-222200002-2-22000000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ68444-4-44-4-4-20-444-4000-2-22-222200002-2-22000000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ6944-44-4-4-44-2-44i4i−4i−4i44-4-22-2222-2−4i4i2-2−2i−2i2i2i2-200000000000000002i−2i00000000000000000000000000000000000000
χ7044-44-4-4-44-2-4−4i−4i4i4i44-4-22-2222-24i−4i2-22i2i−2i−2i2-20000000000000000−2i2i00000000000000000000000000000000000000
χ7144-4-44-44-4-204i−4i4i−4i000-2222-2-220000−2i2i−2i2i0000000000−2i22i222−220000000000−22−22i2−i2i2−i200000000000000000000000000
χ7244-4-44-44-4-204i−4i4i−4i000-2222-2-220000−2i2i−2i2i00000000002i2−2i2−222200000000002−22−2−i2i2−i2i200000000000000000000000000
χ7344-4-44-44-4-20−4i4i−4i4i000-2222-2-2200002i−2i2i−2i0000000000−2i22i2−222200000000002−22−2i2−i2i2−i200000000000000000000000000
χ7444-4-44-44-4-20−4i4i−4i4i000-2222-2-2200002i−2i2i−2i00000000002i2−2i222−220000000000−22−22−i2i2−i2i200000000000000000000000000
χ754-4444-4-4-4440000-44-4-444-44-4-400440000-4-400000000000000000000000000000000000000000000000000000000
χ764-4444-4-4-4-240000-44-42-2-22-22200-2-2000022000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ774-4444-4-4-4-240000-44-42-2-22-22200-2-20000220000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ784-4444-4-4-4-2-400004-442-2-22-22200220000-2-200004i−4i000000000000−2i2i−2i2i0000000000000000000000000000000000
χ794-4444-4-4-4-2-400004-442-2-22-22200220000-2-20000−4i4i0000000000002i−2i2i−2i0000000000000000000000000000000000
χ804-44-4-4-444400000000-44-4-4-44400000000000000000000000000000000000000000000000022−22−222200000000000000
χ814-44-4-4-444400000000-44-4-4-444000000000000000000000000000000000000000000000000−222222−2200000000000000
χ824-4-44-444-44-40000-444-4-444-44-400-4400004-400000000000000000000000000000000000000000000000000000000
χ834-4-44-444-4-2400004-4-422-2-22-2200-2200002-24i−4i0000000000−2i2i−2i2i0000000000000000000000000000000000000000
χ844-4-44-444-4-2400004-4-422-2-22-2200-2200002-2−4i4i00000000002i−2i2i−2i0000000000000000000000000000000000000000
χ854-4-44-444-4-2-40000-44422-2-22-22002-20000-2200000000000000000023−23−23230000000000000000000000000000000000
χ864-4-44-444-4-2-40000-44422-2-22-22002-20000-22000000000000000000−232323−230000000000000000000000000000000000
χ874-4-4-444-44400000000-4-4-444-44000000000000000000000000000000000000000000000000000022−22−22220000000000
χ884-4-4-444-44400000000-4-4-444-440000000000000000000000000000000000000000000000000000−222222−220000000000
χ898-88-8-8-888-4000000004-4444-4-4000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-888-88-400000000444-4-44-4000000000000000000000000000000000000000000000000000000000000000000

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