Finite Group Databasebeta

← Group #10855271

Character table — Group #10855271

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order122222223444444446666666444444121212121212121244888812121212121212121212242424242424242444448888888844121212122244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-111
χ5111111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-11111
χ7111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-11-1-111
χ8111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-111-111-1-1
χ91111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111111-111-1-111111-1-1-1-1-1
χ101111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-11-111-1-1-1-1-1-1-111111
χ111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-11-1-111-1-1111-1-1-111
χ121111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-11-1-11111-1-1-1111-1-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-11-1-111-1-11-1-1-11111
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1111-1-1-1-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11-111-1-1111-1-1-111-1-1
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-111-1-1-1-1-1111-1-111
χ17222222222-22222-2-2-222222220000-2-22222-2-2-2-2000000-2-2000000000000000022220000000000000000-200-20000
χ18222222222-22222-2-2-222222220000-2-22222-2-2-2-2000000-2-20000000000000000-2-2-2-2000000000000000020020000
χ19222222222-2-2-2-2-2-2-2-22222222000022-2-2-2-2-2-2-2-200000022000000000000000022-2-20000000000000000-20020000
χ20222222222-2-2-2-2-2-2-2-22222222000022-2-2-2-2-2-2-2-2000000220000000000000000-2-2220000000000000000200-20000
χ2122222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1111111111111111100000000000022-1-1-1-10000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-222-2-2111111-1-1-1-1-1-1-1-111110000000000002-2-1-1110000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-2-222111111-1-1-1-11111-1-1-1-1000000000000-2211-1-10000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12222-2-211-1-1-1-11111-1-1-1-11111000000000000-2211-1-10000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2-22211-1-1-1-111111111-1-1-1-10000000000002-2-1-1110000000000
χ29222-22-2-2-22-200002-222-2-2-22-2222-2-2000000-2-22200000000000022-2-20000000000002i2i−2i−2i0000000000000000002i−2i
χ30222-22-2-2-22-200002-222-2-2-22-2222-2-2000000-2-22200000000000022-2-2000000000000−2i−2i2i2i000000000000000000−2i2i
χ31222-22-2-2-22-200002-222-2-2-22-22-2-222000000-2-222000000000000-2-2220000000000002i2i−2i−2i000000000000000000−2i2i
χ32222-22-2-2-22-200002-222-2-2-22-22-2-222000000-2-222000000000000-2-222000000000000−2i−2i2i2i0000000000000000002i−2i
χ3322-2-2-2-2222022-2-200022-22-2-2-200000022-2-20000002−22−2000000000022−2−222−2−22i−2i2i−2i−i2i2−i2i2−i2−i2i2i20000000000000000
χ3422-2-2-2-2222022-2-200022-22-2-2-200000022-2-20000002−22−2000000000022−2−222−2−2−2i2i−2i2ii2−i2i2−i2i2i2−i2−i20000000000000000
χ3522-2-2-2-2222022-2-200022-22-2-2-200000022-2-2000000−22−220000000000−2−222−2−2222i−2i2i−2ii2−i2i2−i2i2i2−i2−i20000000000000000
χ3622-2-2-2-2222022-2-200022-22-2-2-200000022-2-2000000−22−220000000000−2−222−2−222−2i2i−2i2i−i2i2−i2i2−i2−i2i2i20000000000000000
χ3722-2-2-2-22220-2-22200022-22-2-2-2000000-2-2220000002−2−22000000000022−2−2−2−2222i−2i−2i2ii2−i2i2−i2−i2−i2i2i20000000000000000
χ3822-2-2-2-22220-2-22200022-22-2-2-2000000-2-2220000002−2−22000000000022−2−2−2−222−2i2i2i−2i−i2i2−i2i2i2i2−i2−i20000000000000000
χ3922-2-2-2-22220-2-22200022-22-2-2-2000000-2-222000000−222−20000000000−2−22222−2−22i−2i−2i2i−i2i2−i2i2i2i2−i2−i20000000000000000
χ4022-2-2-2-22220-2-22200022-22-2-2-2000000-2-222000000−222−20000000000−2−22222−2−2−2i2i2i−2ii2−i2i2−i2−i2−i2i2i20000000000000000
χ412-2-222-22-2222i−2i2i−2i-2-22-222-2-2-222-22-22i−2i2i−2i2i−2i2-22-22i−2i00002i−2i2i2i−2i−2i2-22-2000000000000000000000000000000000000
χ422-2-222-22-2222i−2i2i−2i-2-22-222-2-2-22-22-222i−2i2i−2i2i−2i2-22-2−2i2i00002i−2i−2i−2i2i2i-22-22000000000000000000000000000000000000
χ432-2-222-22-222−2i2i−2i2i-2-22-222-2-2-222-22-2−2i2i−2i2i−2i2i2-22-2−2i2i0000−2i2i−2i−2i2i2i2-22-2000000000000000000000000000000000000
χ442-2-222-22-222−2i2i−2i2i-2-22-222-2-2-22-22-22−2i2i−2i2i−2i2i2-22-22i−2i0000−2i2i2i2i−2i−2i-22-22000000000000000000000000000000000000
χ452-2-222-22-22-22i−2i2i−2i22-2-222-2-2-220000−2i2i2i−2i2i−2i-22-22000000−2i2i00000000000000000000000000000000000002-202i−2i00
χ462-2-222-22-22-22i−2i2i−2i22-2-222-2-2-220000−2i2i2i−2i2i−2i-22-22000000−2i2i0000000000000000000000000000000000000-220−2i2i00
χ472-2-222-22-22-2−2i2i−2i2i22-2-222-2-2-2200002i−2i−2i2i−2i2i-22-220000002i−2i00000000000000000000000000000000000002-20−2i2i00
χ482-2-222-22-22-2−2i2i−2i2i22-2-222-2-2-2200002i−2i−2i2i−2i2i-22-220000002i−2i0000000000000000000000000000000000000-2202i−2i00
χ492-2-222-22-2-122i−2i2i−2i-2-221-1-1111-12-22-22i−2i−ii−ii-11-112i−2i0000−ii−i−iii-11-113−33−3−i3i3−i3i3000000000000003−3−i3i30000000000
χ502-2-222-22-2-122i−2i2i−2i-2-221-1-1111-12-22-22i−2i−ii−ii-11-112i−2i0000−ii−i−iii-11-11−33−33i3−i3i3−i300000000000000−33i3−i30000000000
χ512-2-222-22-2-122i−2i2i−2i-2-221-1-1111-1-22-222i−2i−ii−ii-11-11−2i2i0000−iiii−i−i1-11-13−33−3−i3i3−i3i300000000000000−33i3−i30000000000
χ522-2-222-22-2-122i−2i2i−2i-2-221-1-1111-1-22-222i−2i−ii−ii-11-11−2i2i0000−iiii−i−i1-11-1−33−33i3−i3i3−i3000000000000003−3−i3i30000000000
χ532-2-222-22-2-12−2i2i−2i2i-2-221-1-1111-12-22-2−2i2ii−ii−i-11-11−2i2i0000i−iii−i−i-11-113−33−3i3−i3i3−i3000000000000003−3i3−i30000000000
χ542-2-222-22-2-12−2i2i−2i2i-2-221-1-1111-12-22-2−2i2ii−ii−i-11-11−2i2i0000i−iii−i−i-11-11−33−33−i3i3−i3i300000000000000−33−i3i30000000000
χ552-2-222-22-2-12−2i2i−2i2i-2-221-1-1111-1-22-22−2i2ii−ii−i-11-112i−2i0000i−i−i−iii1-11-13−33−3i3−i3i3−i300000000000000−33−i3i30000000000
χ562-2-222-22-2-12−2i2i−2i2i-2-221-1-1111-1-22-22−2i2ii−ii−i-11-112i−2i0000i−i−i−iii1-11-1−33−33−i3i3−i3i3000000000000003−3i3−i30000000000
χ572-2-2-222-222-20000-222-2-2-22-2222-2-22000000-222-20000000000002-2-2200000000000000002-22-20000002-200000000
χ582-2-2-222-222-20000-222-2-2-22-2222-2-22000000-222-20000000000002-2-220000000000000000-22-22000000-2200000000
χ592-2-2-222-222-20000-222-2-2-22-222-222-2000000-222-2000000000000-222-200000000000000002-22-2000000-2200000000
χ602-2-2-222-222-20000-222-2-2-22-222-222-2000000-222-2000000000000-222-20000000000000000-22-220000002-200000000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-20000-4-4-2-2-2-222220000002200000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-200004422222222000000-2-200000000000000000000000000000000000000000000
χ63444-44-4-4-4440000-44-44-4-4-44-44000000000044-4-40000000000000000000000000000000000000000000000000000
χ64444-44-4-4-4-240000-44-4-2222-22-20000000000-2-2220000000023−2323−230000000000000000000000000000000000000000
χ65444-44-4-4-4-240000-44-4-2222-22-20000000000-2-22200000000−2323−23230000000000000000000000000000000000000000
χ66444-44-4-4-4-2-400004-44-2222-22-244-4-400000022-2-2000000000000-2-222000000000000000000000000000000000000
χ67444-44-4-4-4-2-400004-44-2222-22-2-4-44400000022-2-200000000000022-2-2000000000000000000000000000000000000
χ6844-44-44-4-44000000004-44-4-44-400000000000000000000000000000000000000000022−22−222200000000000000000000
χ6944-44-44-4-44000000004-44-4-44-4000000000000000000000000000000000000000000−222222−2200000000000000000000
χ7044-4-4-4-444-2044-4-4000-2-22-2222000000-2-22200000022−2222−220000000000−2−222−2−2220000000000000000000000000000
χ7144-4-4-4-444-2044-4-4000-2-22-2222000000-2-222000000−2222−2222000000000022−2−222−2−20000000000000000000000000000
χ7244-4-4-4-444-20-4-444000-2-22-222200000022-2-200000022−22−22220000000000−2−22222−2−20000000000000000000000000000
χ7344-4-4-4-444-20-4-444000-2-22-222200000022-2-2000000−222222−22000000000022−2−2−2−2220000000000000000000000000000
χ744-444-4-4-44400000000-4-4444-4-40000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ754-444-4-4-44400000000-4-4444-4-400000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ764-44-4-444-4404i−4i−4i4i000-44-4-444-40000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ774-44-4-444-440−4i4i4i−4i000-44-4-444-4000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ784-44-4-444-4-204i−4i−4i4i0002-222-2-22000000−2i2i2i−2i000000000000000000006−6−66−i6i6i6−i60000000000000000000000000000
χ794-44-4-444-4-204i−4i−4i4i0002-222-2-22000000−2i2i2i−2i00000000000000000000−666−6i6−i6−i6i60000000000000000000000000000
χ804-44-4-444-4-20−4i4i4i−4i0002-222-2-220000002i−2i−2i2i000000000000000000006−6−66i6−i6−i6i60000000000000000000000000000
χ814-44-4-444-4-20−4i4i4i−4i0002-222-2-220000002i−2i−2i2i00000000000000000000−666−6−i6i6i6−i60000000000000000000000000000
χ824-4-444-44-4-2-44i−4i4i−4i44-42-2-2222-20000−4i4i−2i2i−2i2i2-22-20000002i−2i00000000000000000000000000000000000000000000
χ834-4-444-44-4-2-4−4i4i−4i4i44-42-2-2222-200004i−4i2i−2i2i−2i2-22-2000000−2i2i00000000000000000000000000000000000000000000
χ844-4-4-444-444400004-4-4-4-4-44-44400000000004-4-440000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-2400004-4-4222-22-2-20000000000-222-200000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ864-4-4-444-44-2400004-4-4222-22-2-20000000000-222-2000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ874-4-4-444-44-2-40000-444222-22-2-24-4-440000002-2-22000000000000-222-2000000000000000000000000000000000000
χ884-4-4-444-44-2-40000-444222-22-2-2-444-40000002-2-220000000000002-2-22000000000000000000000000000000000000
χ8988-88-88-8-8-400000000-44-444-44000000000000000000000000000000000000000000000000000000000000000000
χ908-888-8-8-88-40000000044-4-4-444000000000000000000000000000000000000000000000000000000000000000000

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