Finite Group Databasebeta

← Group #10863772

Character table — Group #10863772

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
χ311111111111111111111111111-1-1-1-111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1111
χ51111111111111111111111-1-1-1-11111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-11-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11111-111-1
χ911111111111111111111-1-11111111111-1-1-1-1111111-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-111-1-11111-1-1-1-1-1-1
χ1011111111111111111111-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ1111111111111111111111-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-111-1-111-1-1-1111
χ1211111111111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-111111-1-11111-1-1111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111111-1-111-1-1-1-111-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-11-1-1111111-1-1111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-111-1-111-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-111-1-1-1-11111-1-1-1-1-1-1111111-1-11111-111-1-1-1-111-1-11-1-11
χ17222222222-2-2-2-222222222200000000-2-22222-2-222220000-20000000000-2-20000000022-2-2000000000000000-2000
χ18222222222-2-2-2-222222222200000000-2-22222-2-2-2-2-2-20000-20000000000-2-200000000-2-2220000000000000002000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222220000200000000002200000000-2-2-2-20000000000000002000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-200002000000000022000000002222000000000000000-2000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1000022-2-22-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-10000-2-2-2-222211111111-1-1-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-2-211111111-1-111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-11111-1-10000-2-222-2-2-2-1-1-1-1111111-1-1-1-1111100000000-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-11111-1-10000-2-2-2-2-222-1-1-1-11111111111-1-1-1-100000000211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-1000022-2-2-2-2-21111-1-1-1-111-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-100002222-2221111-1-1-1-1111111-1-1-1-100000000-2-1-1110000000000
χ29222-2-2-22-22-2-222-22-222-2-2002i2i−2i−2i2i2i−2i−2i2-200002-20000002-20002i2i−2i−2i0000002i2i−2i−2i00000000000002-2000000000000
χ30222-2-2-22-22-2-222-22-222-2-2002i2i−2i−2i−2i−2i2i2i2-200002-2000000-220002i2i−2i−2i000000−2i−2i2i2i0000000000000-22000000000000
χ31222-2-2-22-22-2-222-22-222-2-200−2i−2i2i2i2i2i−2i−2i2-200002-2000000-22000−2i−2i2i2i0000002i2i−2i−2i0000000000000-22000000000000
χ32222-2-2-22-22-2-222-22-222-2-200−2i−2i2i2i−2i−2i2i2i2-200002-20000002-2000−2i−2i2i2i000000−2i−2i2i2i00000000000002-2000000000000
χ33222-2-2-22-2-1-2-2221-11-1-111002i2i−2i−2i2i2i−2i−2i-1133−3−3-110000002-2000−i−iii−i3−i3i3i33−3−i−iii−i3−i3i3i3000000000-113−30000000000
χ34222-2-2-22-2-1-2-2221-11-1-111002i2i−2i−2i2i2i−2i−2i-11−3−333-110000002-2000−i−iiii3i3−i3−i3−33−i−iiii3i3−i3−i3000000000-11−330000000000
χ35222-2-2-22-2-1-2-2221-11-1-111002i2i−2i−2i−2i−2i2i2i-1133−3−3-11000000-22000−i−iii−i3−i3i3i33−3ii−i−ii3i3−i3−i30000000001-1−330000000000
χ36222-2-2-22-2-1-2-2221-11-1-111002i2i−2i−2i−2i−2i2i2i-11−3−333-11000000-22000−i−iiii3i3−i3−i3−33ii−i−i−i3−i3i3i30000000001-13−30000000000
χ37222-2-2-22-2-1-2-2221-11-1-11100−2i−2i2i2i2i2i−2i−2i-1133−3−3-11000000-22000ii−i−ii3i3−i3−i33−3−i−iii−i3−i3i3i30000000001-1−330000000000
χ38222-2-2-22-2-1-2-2221-11-1-11100−2i−2i2i2i2i2i−2i−2i-11−3−333-11000000-22000ii−i−i−i3−i3i3i3−33−i−iiii3i3−i3−i30000000001-13−30000000000
χ39222-2-2-22-2-1-2-2221-11-1-11100−2i−2i2i2i−2i−2i2i2i-1133−3−3-110000002-2000ii−i−ii3i3−i3−i33−3ii−i−ii3i3−i3−i3000000000-113−30000000000
χ40222-2-2-22-2-1-2-2221-11-1-11100−2i−2i2i2i−2i−2i2i2i-11−3−333-110000002-2000ii−i−i−i3−i3i3i3−33ii−i−i−i3−i3i3i3000000000-11−330000000000
χ4122-2-2-22-2220000-2-222-22-22-20000−i2i2−i2i2002-22-2002i2i−2i−2i00000−i2i20000000000−i2i2−i2i2−i2i2−i2i22i−2i0022−2−20000000000002−20
χ4222-2-2-22-2220000-2-222-22-22-20000−i2i2−i2i2002-22-200−2i−2i2i2i00000−i2i20000000000−i2i2−i2i2−i2i2−i2i2−2i2i00−2−222000000000000−220
χ4322-2-2-22-2220000-2-222-22-22-20000i2−i2i2−i2002-22-2002i2i−2i−2i00000i2−i20000000000i2−i2i2−i2i2−i2i2−i22i−2i00−2−222000000000000−220
χ4422-2-2-22-2220000-2-222-22-22-20000i2−i2i2−i2002-22-200−2i−2i2i2i00000i2−i20000000000i2−i2i2−i2i2−i2i2−i2−2i2i0022−2−20000000000002−20
χ4522-2-2-22-2220000-2-222-22-2-220000−i2i2−i2i200-22-22002i2i−2i−2i00000i2−i20000000000−i2i2−i2i2i2−i2i2−i2−2i2i0022−2−2000000000000−220
χ4622-2-2-22-2220000-2-222-22-2-220000−i2i2−i2i200-22-2200−2i−2i2i2i00000i2−i20000000000−i2i2−i2i2i2−i2i2−i22i−2i00−2−2220000000000002−20
χ4722-2-2-22-2220000-2-222-22-2-220000i2−i2i2−i200-22-22002i2i−2i−2i00000−i2i20000000000i2−i2i2−i2−i2i2−i2i2−2i2i00−2−2220000000000002−20
χ4822-2-2-22-2220000-2-222-22-2-220000i2−i2i2−i200-22-2200−2i−2i2i2i00000−i2i20000000000i2−i2i2−i2−i2i2−i2i22i−2i0022−2−2000000000000−220
χ492-2-22-222-222-2-22-222-2-2-220000000000-2200002-22i−2i2i−2i2i−2i0000000002i−2i2i−2i0000000000002i−2i00000000000002-20000
χ502-2-22-222-222-2-22-222-2-2-220000000000-2200002-22i−2i2i−2i−2i2i000000000−2i2i−2i2i0000000000002i−2i0000000000000-220000
χ512-2-22-222-222-2-22-222-2-2-220000000000-2200002-2−2i2i−2i2i2i−2i0000000002i−2i2i−2i000000000000−2i2i0000000000000-220000
χ522-2-22-222-222-2-22-222-2-2-220000000000-2200002-2−2i2i−2i2i−2i2i000000000−2i2i−2i2i000000000000−2i2i00000000000002-20000
χ532-2-22-222-22-222-2-222-2-2-22002i−2i2i−2i00002-20000-222i−2i2i−2i00000002i−2i2i−2i0000000000000000−2i2i000000000002-2000000
χ542-2-22-222-22-222-2-222-2-2-22002i−2i2i−2i00002-20000-22−2i2i−2i2i00000002i−2i2i−2i00000000000000002i−2i00000000000-22000000
χ552-2-22-222-22-222-2-222-2-2-2200−2i2i−2i2i00002-20000-222i−2i2i−2i0000000−2i2i−2i2i0000000000000000−2i2i00000000000-22000000
χ562-2-22-222-22-222-2-222-2-2-2200−2i2i−2i2i00002-20000-22−2i2i−2i2i0000000−2i2i−2i2i00000000000000002i−2i000000000002-2000000
χ572-2-2-22-22222-22-222-2-2-22-2002-2-220000220000-2-2000000000002-2-220000000000000000002i−2i2i−2i000002i−2i00000000
χ582-2-2-22-22222-22-222-2-2-22-2002-2-220000220000-2-2000000000002-2-22000000000000000000−2i2i−2i2i00000−2i2i00000000
χ592-2-2-22-22222-22-222-2-2-22-200-222-20000220000-2-200000000000-222-20000000000000000002i−2i2i−2i00000−2i2i00000000
χ602-2-2-22-22222-22-222-2-2-22-200-222-20000220000-2-200000000000-222-2000000000000000000−2i2i−2i2i000002i−2i00000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2440000000022-2-2-2-22200000000-40000000000220000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400000000222222220000000040000000000-2-20000000000000000000000000000000
χ63444-4-4-44-4444-4-4-44-444-4-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ64444-4-4-44-4-244-4-42-22-2-22200000000002-22323−23−232-20000000000000000000−23230000000000000000000000000000000
χ65444-4-4-44-4-244-4-42-22-2-22200000000002-2−23−2323232-2000000000000000000023−230000000000000000000000000000000
χ6644-444-4-4-4400004-4-44-4-4400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ6744-444-4-4-4400004-4-44-4-44000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ6844-444-4-4-4-20000-222-222-200000022−22−22220023−23−232300000000000000000000000−222−2−666−600000000000000000000000
χ6944-444-4-4-4-20000-222-222-200000022−22−222200−232323−2300000000000000000000000−222−26−6−6600000000000000000000000
χ7044-444-4-4-4-20000-222-222-2000000−222222−220023−23−2323000000000000000000000002−2−226−6−6600000000000000000000000
χ7144-444-4-4-4-20000-222-222-2000000−222222−2200−232323−23000000000000000000000002−2−22−666−600000000000000000000000
χ7244-4-4-44-44-2000022-2-22-224-40000−2i22i2−2i22i200-22-2200000000000−2i22i20000000000i2−i2i2−i2i2−i2i2−i200000000000000000000000
χ7344-4-4-44-44-2000022-2-22-224-400002i2−2i22i2−2i200-22-22000000000002i2−2i20000000000−i2i2−i2i2−i2i2−i2i200000000000000000000000
χ7444-4-4-44-44-2000022-2-22-22-440000−2i22i2−2i22i2002-22-2000000000002i2−2i20000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000
χ7544-4-4-44-44-2000022-2-22-22-4400002i2−2i22i2−2i2002-22-200000000000−2i22i20000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000
χ764-444-4-4-4440000-4-4-4-4444000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ774-444-4-4-4440000-4-4-4-44440000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ784-44-444-4-4400004-44-44-4-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ794-44-444-4-4400004-44-44-4-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ804-4-44-444-4-24-4-442-2-2222-200000000002-20000-2200004i−4i000000000−2i2i−2i2i000000000000000000000000000000000
χ814-4-44-444-4-24-4-442-2-2222-200000000002-20000-220000−4i4i0000000002i−2i2i−2i000000000000000000000000000000000
χ824-4-44-444-4-2-444-42-2-2222-2004i−4i4i−4i0000-2200002-200000000000−2i2i−2i2i0000000000000000000000000000000000000
χ834-4-44-444-4-2-444-42-2-2222-200−4i4i−4i4i0000-2200002-2000000000002i−2i2i−2i0000000000000000000000000000000000000
χ844-4-4-44-4444-44-4444-4-4-44-40000000000-4-40000440000000000000000000000000000000000000000000000000000
χ854-4-4-44-444-24-44-4-2-2222-22004-4-440000-2-200002200000000000-222-20000000000000000000000000000000000000
χ864-4-4-44-444-24-44-4-2-2222-2200-444-40000-2-2000022000000000002-2-220000000000000000000000000000000000000
χ874-4-4-44-444-2-44-44-2-2222-220000000000220000-2-200000000000000023−23−2323000000000000000000000000000000000
χ884-4-4-44-444-2-44-44-2-2222-220000000000220000-2-2000000000000000−232323−23000000000000000000000000000000000
χ898-888-8-8-88-400004444-4-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-888-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000

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