Finite Group Databasebeta

← Group #10898397

Character table — Group #10898397

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344446666666444488881212121212121212224466668812121212121224242424242424244444888844121212124444448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1
χ911111111111111111111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-1-111-1-111-1-1-1-11-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11111-11
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1111-1-1-1-1-1-111-1-1-11
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1111-1
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1-111-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-111-1-111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11-1-1-111-1-1-1-111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111-1-1-1111111-1-1-1-1-11
χ17222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-200000000002200000000000022-2-200000000002-200000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-2000000000022000000000000-2-2220000000000-2200000000
χ19222222222-2-2-2-22222222-2-2220000-2-22222-2-20000000000-2-200000000000022-2-20000000000-2200000000
χ20222222222-2-2-2-22222222-2-2220000-2-22222-2-20000000000-2-2000000000000-2-22200000000002-200000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2-2-2111122-1-11111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-1-1-1-1-1-11111111100000000-2-211110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-1-11111111111110000000022-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-122-2-2-1-1-1-1-2-2111111-1-1-1-11111000000002-211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-1-2-2221111-2-211-1-1-1-1-1-1-1-1111100000000-22-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-122-2-2-1-1-1-1221111111111-1-1-1-100000000-22-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1-2-22211112211-1-1-1-11111-1-1-1-1000000002-211-1-10000000000
χ29222-22-2-2-222-22-2-2-2-22-222000000002-200002-22-20022-2-200000000000000002i−2i2i−2i0000000000002i−2i000000
χ30222-22-2-2-222-22-2-2-2-22-222000000002-200002-22-20022-2-20000000000000000−2i2i−2i2i000000000000−2i2i000000
χ31222-22-2-2-222-22-2-2-2-22-222000000002-200002-2-2200-2-22200000000000000002i−2i2i−2i000000000000−2i2i000000
χ32222-22-2-2-222-22-2-2-2-22-222000000002-200002-2-2200-2-2220000000000000000−2i2i−2i2i0000000000002i−2i000000
χ33222-22-2-2-22-22-22-2-2-22-22200000000-220000-22002-20000000022-2-2000000002i−2i−2i2i000000000000002i−2i0000
χ34222-22-2-2-22-22-22-2-2-22-22200000000-220000-22002-20000000022-2-200000000−2i2i2i−2i00000000000000−2i2i0000
χ35222-22-2-2-22-22-22-2-2-22-22200000000-220000-2200-2200000000-2-222000000002i−2i−2i2i00000000000000−2i2i0000
χ36222-22-2-2-22-22-22-2-2-22-22200000000-220000-2200-2200000000-2-22200000000−2i2i2i−2i000000000000002i−2i0000
χ372-22-2-222-222-2-2222-2-2-22-22i−2i2i−2i00002-22i2i−2i−2i-2200000000002i−2i000000000000000022-2-20000000000002i−2i00
χ382-22-2-222-222-2-2222-2-2-22-22i−2i2i−2i00002-22i2i−2i−2i-2200000000002i−2i0000000000000000-2-222000000000000−2i2i00
χ392-22-2-222-222-2-2222-2-2-22-2−2i2i−2i2i00002-2−2i−2i2i2i-220000000000−2i2i000000000000000022-2-2000000000000−2i2i00
χ402-22-2-222-222-2-2222-2-2-22-2−2i2i−2i2i00002-2−2i−2i2i2i-220000000000−2i2i0000000000000000-2-2220000000000002i−2i00
χ412-22-2-222-22-222-222-2-2-22-22i−2i−2i2i22-2-2-22−2i−2i2i2i2-2000000002i−2i2i−2i000022-2-22i2i−2i−2i000000000000000000000000
χ422-22-2-222-22-222-222-2-2-22-22i−2i−2i2i-2-222-22−2i−2i2i2i2-200000000−2i2i2i−2i0000-2-222−2i−2i2i2i000000000000000000000000
χ432-22-2-222-22-222-222-2-2-22-2−2i2i2i−2i22-2-2-222i2i−2i−2i2-200000000−2i2i−2i2i000022-2-2−2i−2i2i2i000000000000000000000000
χ442-22-2-222-22-222-222-2-2-22-2−2i2i2i−2i-2-222-222i2i−2i−2i2-2000000002i−2i−2i2i0000-2-2222i2i−2i−2i000000000000000000000000
χ452-22-2-222-2-1-222-2-1-1111-112i−2i−2i2i22-2-21-1ii−i−i-110000−i3i3−i3i32i−2i−ii3−33−3-1-111−i−iii00000000003−3−i3i30000000000
χ462-22-2-222-2-1-222-2-1-1111-112i−2i−2i2i22-2-21-1ii−i−i-110000i3−i3i3−i32i−2i−ii−33−33-1-111−i−iii0000000000−33i3−i30000000000
χ472-22-2-222-2-1-222-2-1-1111-112i−2i−2i2i-2-2221-1ii−i−i-110000−i3i3−i3i3−2i2i−ii3−33−311-1-1ii−i−i0000000000−33i3−i30000000000
χ482-22-2-222-2-1-222-2-1-1111-112i−2i−2i2i-2-2221-1ii−i−i-110000i3−i3i3−i3−2i2i−ii−33−3311-1-1ii−i−i00000000003−3−i3i30000000000
χ492-22-2-222-2-1-222-2-1-1111-11−2i2i2i−2i22-2-21-1−i−iii-110000−i3i3−i3i3−2i2ii−i−33−33-1-111ii−i−i0000000000−33−i3i30000000000
χ502-22-2-222-2-1-222-2-1-1111-11−2i2i2i−2i22-2-21-1−i−iii-110000i3−i3i3−i3−2i2ii−i3−33−3-1-111ii−i−i00000000003−3i3−i30000000000
χ512-22-2-222-2-1-222-2-1-1111-11−2i2i2i−2i-2-2221-1−i−iii-110000−i3i3−i3i32i−2ii−i−33−3311-1-1−i−iii00000000003−3i3−i30000000000
χ522-22-2-222-2-1-222-2-1-1111-11−2i2i2i−2i-2-2221-1−i−iii-110000i3−i3i3−i32i−2ii−i3−33−311-1-1−i−iii0000000000−33−i3i30000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000222222220000000000-2-2000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444000022-2-2-2-222000000000022000000000000000000000000000000000000
χ55444-44-4-4-4-24-44-4222-22-2-200000000-220000-224-400-2-2220000000000000000000000000000000000000000
χ56444-44-4-4-4-24-44-4222-22-2-200000000-220000-22-440022-2-20000000000000000000000000000000000000000
χ57444-44-4-4-4-2-44-44222-22-2-2000000002-200002-2004-400000000-2-22200000000000000000000000000000000
χ58444-44-4-4-4-2-44-44222-22-2-2000000002-200002-200-440000000022-2-200000000000000000000000000000000
χ5944-44-44-4-4400004-444-4-4-40000000000000000000000000000000000000000000022−2222−220000000000000000
χ6044-44-44-4-4400004-444-4-4-400000000000000000000000000000000000000000000−2222−22220000000000000000
χ6144-4-4-4-44440000-44-444-4-40000−2i22i2−2i22i2000000000000000000000000−2i22i2−2i22i20000000000000000000000000000
χ6244-4-4-4-44440000-44-444-4-400002i2−2i22i2−2i20000000000000000000000002i2−2i22i2−2i20000000000000000000000000000
χ6344-4-4-4-444-200002-22-2-2220000−2i22i2−2i22i20023−2323−23000000000000000000i2−i2i2−i2i6−i6i6−i6000000000000000000000000
χ6444-4-4-4-444-200002-22-2-2220000−2i22i2−2i22i200−2323−2323000000000000000000i2−i2i2−i2−i6i6−i6i6000000000000000000000000
χ6544-4-4-4-444-200002-22-2-22200002i2−2i22i2−2i20023−2323−23000000000000000000−i2i2−i2i2−i6i6−i6i6000000000000000000000000
χ6644-4-4-4-444-200002-22-2-22200002i2−2i22i2−2i200−2323−2323000000000000000000−i2i2−i2i2i6−i6i6−i6000000000000000000000000
χ674-444-4-4-44444-4-4-4-44-444-400000000440000-4-4000000000000000000000000000000000000000000000000
χ684-444-4-4-444-4-444-4-44-444-400000000-4-4000044000000000000000000000000000000000000000000000000
χ694-444-4-4-44-244-4-422-22-2-2200000000-2-200002200000000000023−23−232300000000000000000000000000000000
χ704-444-4-4-44-244-4-422-22-2-2200000000-2-2000022000000000000−232323−2300000000000000000000000000000000
χ714-444-4-4-44-2-4-44422-22-2-2200000000220000-2-20000−2i32i32i3−2i30000000000000000000000000000000000000000
χ724-444-4-4-44-2-4-44422-22-2-2200000000220000-2-200002i3−2i3−2i32i30000000000000000000000000000000000000000
χ734-44-4-444-4-24-4-44-2-2222-224i−4i4i−4i0000-22−2i−2i2i2i2-20000000000−2i2i000000000000000000000000000000000000
χ744-44-4-444-4-24-4-44-2-2222-22−4i4i−4i4i0000-222i2i−2i−2i2-200000000002i−2i000000000000000000000000000000000000
χ754-4-444-44-440000-444-4-4-440000−2i22i22i2−2i2000000000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ764-4-444-44-440000-444-4-4-4400002i2−2i2−2i22i20000000000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ774-4-444-44-4-200002-2-2222-20000−2i22i22i2−2i200−2i32i32i3−2i3000000000000000000i2−i2−i2i2−666−6000000000000000000000000
χ784-4-444-44-4-200002-2-2222-20000−2i22i22i2−2i2002i3−2i3−2i32i3000000000000000000i2−i2−i2i26−6−66000000000000000000000000
χ794-4-444-44-4-200002-2-2222-200002i2−2i2−2i22i200−2i32i32i3−2i3000000000000000000−i2i2i2−i26−6−66000000000000000000000000
χ804-4-444-44-4-200002-2-2222-200002i2−2i2−2i22i2002i3−2i3−2i32i3000000000000000000−i2i2i2−i2−666−6000000000000000000000000
χ814-4-4-444-44400004-4-4-44-440000000000000000000000000000000000000000000022−22−22220000000000000000
χ824-4-4-444-44400004-4-4-44-4400000000000000000000000000000000000000000000−222222−220000000000000000
χ8388-88-88-8-8-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-888-88-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000

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