Finite Group Databasebeta

← Group #10853378

Character table — Group #10853378

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-11111111-1-1-1-111111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-111-1-1-1-1-11111-1-1-1
χ6111111111111111111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1111-1-1-1-1111
χ7111111111111111111111111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-111-1-1111
χ8111111111111111111111111-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-111111-1-111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-11-1-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-111-1
χ1311111111111111111111-1-1-1-1-1-11111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111111-1-111-111-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-11-1-1111-1-1111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-111-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-111-11111-1-1-1-11111-1-1-1-1-1-11111-1-1111111-111-1-11-1-111-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-2-22222-2222200-2000000000000-2-200000000-2-222000000000-2000000000
χ18222222222-2-2-2-222222220000220000-2-2-22222-2-2-2-2-200-2000000000000-2-20000000022-2-20000000002000000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220020000000000002200000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-200200000000000022000000002222000000000-2000000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-1-11111-10000-2-2-222-2-2-1-1-1-1111111-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-11111-10000-2-2-2-2-222-1-1-1-11111111111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-22-2-22211111111-1-1-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-2-211111111-1-111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-11111-1000022-2-2-2-2-21111-1-1-1-111-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-1-11111-1000022-222221111-1-1-1-1111111-1-1-1-100000000-2-1-1110000000000
χ29222-2-22-2-2222-2-22-222-2-2-222-2-200000022-20000-222-2-2000000022-2-2000000000000002-2000000000000002-200000
χ30222-2-22-2-2222-2-22-222-2-2-222-2-200000022-20000-2-2-222000000022-2-200000000000000-2200000000000000-2200000
χ31222-2-22-2-2222-2-22-222-2-2-2-2-22200000022-20000-222-2-20000000-2-222000000000000002-200000000000000-2200000
χ32222-2-22-2-2222-2-22-222-2-2-2-2-22200000022-20000-2-2-2220000000-2-22200000000000000-22000000000000002-200000
χ33222-2-22-2-22-2-2222-222-2-2-20000000000-2-220000222-2-22i−2i0000000002i2i−2i−2i0000000000-220000000000002i−2i0000000
χ34222-2-22-2-22-2-2222-222-2-2-20000000000-2-220000222-2-2−2i2i000000000−2i−2i2i2i0000000000-22000000000000−2i2i0000000
χ35222-2-22-2-22-2-2222-222-2-2-20000000000-2-2200002-2-2222i−2i0000000002i2i−2i−2i00000000002-2000000000000−2i2i0000000
χ36222-2-22-2-22-2-2222-222-2-2-20000000000-2-2200002-2-222−2i2i000000000−2i−2i2i2i00000000002-20000000000002i−2i0000000
χ372-222-2-2-2220000-22-22-22-200002i−2i22−2−20002i2i−2i−2i02i−2i2i−2i00000−i2i2000000000022−2−2−i2−i2i2i2002-2−i2−i2i2i20000000000002−20
χ382-222-2-2-2220000-22-22-22-200002i−2i22−2−20002i2i−2i−2i0−2i2i−2i2i00000−i2i2000000000022−2−2−i2−i2i2i200-22i2i2−i2−i2000000000000−220
χ392-222-2-2-2220000-22-22-22-200002i−2i−2−2220002i2i−2i−2i02i−2i2i−2i00000i2−i20000000000−2−222i2i2−i2−i2002-2i2i2−i2−i2000000000000−220
χ402-222-2-2-2220000-22-22-22-200002i−2i−2−2220002i2i−2i−2i0−2i2i−2i2i00000i2−i20000000000−2−222i2i2−i2−i200-22−i2−i2i2i20000000000002−20
χ412-222-2-2-2220000-22-22-22-20000−2i2i22−2−2000−2i−2i2i2i02i−2i2i−2i00000i2−i2000000000022−2−2i2i2−i2−i200-22−i2−i2i2i2000000000000−220
χ422-222-2-2-2220000-22-22-22-20000−2i2i22−2−2000−2i−2i2i2i0−2i2i−2i2i00000i2−i2000000000022−2−2i2i2−i2−i2002-2i2i2−i2−i20000000000002−20
χ432-222-2-2-2220000-22-22-22-20000−2i2i−2−222000−2i−2i2i2i02i−2i2i−2i00000−i2i20000000000−2−222−i2−i2i2i200-22i2i2−i2−i20000000000002−20
χ442-222-2-2-2220000-22-22-22-20000−2i2i−2−222000−2i−2i2i2i0−2i2i−2i2i00000−i2i20000000000−2−222−i2−i2i2i2002-2−i2−i2i2i2000000000000−220
χ452-2-22-222-222-2-22-222-22-2-22i−2i2i−2i0000002-2-200002000000000002i−2i2i−2i0000000000000000002i−2i2i−2i00000000002-2000
χ462-2-22-222-222-2-22-222-22-2-22i−2i2i−2i0000002-2-200002000000000002i−2i2i−2i000000000000000000−2i2i−2i2i0000000000-22000
χ472-2-22-222-222-2-22-222-22-2-2−2i2i−2i2i0000002-2-20000200000000000−2i2i−2i2i0000000000000000002i−2i2i−2i0000000000-22000
χ482-2-22-222-222-2-22-222-22-2-2−2i2i−2i2i0000002-2-20000200000000000−2i2i−2i2i000000000000000000−2i2i−2i2i00000000002-2000
χ492-2-2-222-2222-22-2-2-22-2-2222i−2i−2i2i002i−2i2i−2i2-220000-200000002-2002i−2i−2i2i0000002i−2i2i−2i00000000000002-2000000000000
χ502-2-2-222-2222-22-2-2-22-2-2222i−2i−2i2i00−2i2i−2i2i2-220000-20000000-22002i−2i−2i2i000000−2i2i−2i2i0000000000000-22000000000000
χ512-2-2-222-2222-22-2-2-22-2-222−2i2i2i−2i002i−2i2i−2i2-220000-20000000-2200−2i2i2i−2i0000002i−2i2i−2i0000000000000-22000000000000
χ522-2-2-222-2222-22-2-2-22-2-222−2i2i2i−2i00−2i2i−2i2i2-220000-200000002-200−2i2i2i−2i000000−2i2i−2i2i00000000000002-2000000000000
χ532-2-2-222-22-12-22-211-111-1-12i−2i−2i2i002i−2i2i−2i-11-1−i3i3−i3i3100000002-200−iii−i3−33−3−i3i3−ii−ii3−33−3000000000-11−i3i30000000000
χ542-2-2-222-22-12-22-211-111-1-12i−2i−2i2i002i−2i2i−2i-11-1i3−i3i3−i3100000002-200−iii−i−33−33i3−i3−ii−ii−33−33000000000-11i3−i30000000000
χ552-2-2-222-22-12-22-211-111-1-12i−2i−2i2i00−2i2i−2i2i-11-1−i3i3−i3i310000000-2200−iii−i3−33−3−i3i3i−ii−i−33−330000000001-1i3−i30000000000
χ562-2-2-222-22-12-22-211-111-1-12i−2i−2i2i00−2i2i−2i2i-11-1i3−i3i3−i310000000-2200−iii−i−33−33i3−i3i−ii−i3−33−30000000001-1−i3i30000000000
χ572-2-2-222-22-12-22-211-111-1-1−2i2i2i−2i002i−2i2i−2i-11-1−i3i3−i3i310000000-2200i−i−ii−33−33−i3i3−ii−ii3−33−30000000001-1i3−i30000000000
χ582-2-2-222-22-12-22-211-111-1-1−2i2i2i−2i002i−2i2i−2i-11-1i3−i3i3−i310000000-2200i−i−ii3−33−3i3−i3−ii−ii−33−330000000001-1−i3i30000000000
χ592-2-2-222-22-12-22-211-111-1-1−2i2i2i−2i00−2i2i−2i2i-11-1−i3i3−i3i3100000002-200i−i−ii−33−33−i3i3i−ii−i−33−33000000000-11−i3i30000000000
χ602-2-2-222-22-12-22-211-111-1-1−2i2i2i−2i00−2i2i−2i2i-11-1i3−i3i3−i3100000002-200i−i−ii3−33−3i3−i3i−ii−i3−33−3000000000-11i3−i30000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-20000440000222-2-2-2-22000000-4000000000000220000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-40000222222220000004000000000000-2-20000000000000000000000000000000
χ63444-4-44-4-4-244-4-4-22-2-222244-4-4000000-2-220000200000000000-2-2220000000000000000000000000000000000000
χ64444-4-44-4-4-244-4-4-22-2-2222-4-444000000-2-22000020000000000022-2-20000000000000000000000000000000000000
χ65444-4-44-4-4-2-4-444-22-2-2222000000000022-20000-200004i−4i000000000−2i−2i2i2i000000000000000000000000000000000
χ66444-4-44-4-4-2-4-444-22-2-2222000000000022-20000-20000−4i4i0000000002i2i−2i−2i000000000000000000000000000000000
χ6744-444-4-4-44000044-4-4-4-4400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ6844-444-4-4-44000044-4-4-4-44000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ6944-4-4-4-444400004-4-4-444-4000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ7044-4-4-4-444400004-4-4-444-40000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ7144-4-4-4-444-20000-2222-2-22000000−2i22i22i2−2i200023−23−23230000000000000000000000i2−i2−i2i2i6−i6−i6i600000000000000000000000
χ7244-4-4-4-444-20000-2222-2-22000000−2i22i22i2−2i2000−232323−230000000000000000000000i2−i2−i2i2−i6i6i6−i600000000000000000000000
χ7344-4-4-4-444-20000-2222-2-220000002i2−2i2−2i22i200023−23−23230000000000000000000000−i2i2i2−i2−i6i6i6−i600000000000000000000000
χ7444-4-4-4-444-20000-2222-2-220000002i2−2i2−2i22i2000−232323−230000000000000000000000−i2i2i2−i2i6−i6−i6i600000000000000000000000
χ754-444-4-4-44-200002-22-22-2200004i−4i2222−22−22000−2i−2i2i2i0000000000−2i22i20000000000−2−222i2i2−i2−i200000000000000000000000
χ764-444-4-4-44-200002-22-22-2200004i−4i−22−222222000−2i−2i2i2i00000000002i2−2i2000000000022−2−2−i2−i2i2i200000000000000000000000
χ774-444-4-4-44-200002-22-22-220000−4i4i2222−22−220002i2i−2i−2i00000000002i2−2i20000000000−2−222−i2−i2i2i200000000000000000000000
χ784-444-4-4-44-200002-22-22-220000−4i4i−22−2222220002i2i−2i−2i0000000000−2i22i2000000000022−2−2i2i2−i2−i200000000000000000000000
χ794-44-44-44-440000-4-4-444-440000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ804-44-44-44-440000-4-4-444-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ814-4-44-444-44-444-4-444-44-4-40000000000-4440000-40000000000000000000000000000000000000000000000000000
χ824-4-44-444-4-24-4-442-2-22-2224i−4i4i−4i000000-2220000-200000000000−2i2i−2i2i0000000000000000000000000000000000000
χ834-4-44-444-4-24-4-442-2-22-222−4i4i−4i4i000000-2220000-2000000000002i−2i2i−2i0000000000000000000000000000000000000
χ844-4-44-444-4-2-444-42-2-22-22200000000002-2-200002000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ854-4-44-444-4-2-444-42-2-22-22200000000002-2-2000020000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ864-4-4-444-444-44-44-4-44-4-4440000000000-44-4000040000000000000000000000000000000000000000000000000000
χ874-4-4-444-44-2-44-4422-222-2-200000000002-22−2i32i3−2i32i3-200000000000000000002i3−2i30000000000000000000000000000000
χ884-4-4-444-44-2-44-4422-222-2-200000000002-222i3−2i32i3−2i3-20000000000000000000−2i32i30000000000000000000000000000000
χ8988-888-8-8-8-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-88-88-8-40000444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000

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