Finite Group Databasebeta

← Group #10900968

Character table — Group #10900968

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order1222222234444444466666662212121212121212124444668888121212121212121224242424242424244444444444121212124444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-111-1-111-1-111-1-11-1
χ10111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111-111-1-1-1-111-1-111-11
χ11111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11-1-11111-1-1-1-111-11
χ12111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-11-1-111-1-11111-1-11-1
χ13111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-11-1-111-1-11111-1-1-11
χ14111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-11-1-11111-1-1-1-1111-1
χ15111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-11-111-1-1-1-111-1-1111-1
χ16111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1111-111-1-111-1-111-1-1-11
χ172222222222222-2-2-2-22222222-2-2-2-22222-2-20000-2-20000000000000000000022-2-2-2-2220000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-22222-2-20000-2-200000000000000000000-2-22222-2-20000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000022000000000000000000002222-2-2-2-20000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200002200000000000000000000-2-2-2-222220000000000000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-1222211111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-211111111111111110000000022-1-1-1-10000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-21122-2-2-1-1-1-11111-1-1-1-11111000000002-2-1-1110000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-211-2-222-1-1-1-111111111-1-1-1-100000000-2211-1-10000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-2221122-2-21111-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-22211-2-2221111-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ2922-22-2-22-222i2i−2i−2i00002-222-2-2-200002i2i−2i−2i000000002−2−i2i20000000022−2−2−i2−i2i2i22-200002i−2i00000000002−2−i2i200
χ3022-22-2-22-222i2i−2i−2i00002-222-2-2-200002i2i−2i−2i000000002−2−i2i20000000022−2−2−i2−i2i2i2-220000−2i2i0000000000−22i2−i200
χ3122-22-2-22-222i2i−2i−2i00002-222-2-2-200002i2i−2i−2i00000000−22i2−i200000000−2−222i2i2−i2−i22-200002i−2i0000000000−22i2−i200
χ3222-22-2-22-222i2i−2i−2i00002-222-2-2-200002i2i−2i−2i00000000−22i2−i200000000−2−222i2i2−i2−i2-220000−2i2i00000000002−2−i2i200
χ3322-22-2-22-22−2i−2i2i2i00002-222-2-2-20000−2i−2i2i2i000000002−2i2−i20000000022−2−2i2i2−i2−i22-20000−2i2i00000000002−2i2−i200
χ3422-22-2-22-22−2i−2i2i2i00002-222-2-2-20000−2i−2i2i2i000000002−2i2−i20000000022−2−2i2i2−i2−i2-2200002i−2i0000000000−22−i2i200
χ3522-22-2-22-22−2i−2i2i2i00002-222-2-2-20000−2i−2i2i2i00000000−22−i2i200000000−2−222−i2−i2i2i22-20000−2i2i0000000000−22−i2i200
χ3622-22-2-22-22−2i−2i2i2i00002-222-2-2-20000−2i−2i2i2i00000000−22−i2i200000000−2−222−i2−i2i2i2-2200002i−2i00000000002−2i2−i200
χ372-2-2-22-22222-22-222-2-2-2-22-222-22-2-2-22-22-22200002-200000000000000000000000000000000002-22-2000000
χ382-2-2-22-22222-22-222-2-2-2-22-222-22-2-2-22-22-22200002-20000000000000000000000000000000000-22-22000000
χ392-2-2-22-22222-22-2-2-222-2-22-222-2-22222-22-2-2-22-22-2-22000022-2-222-2-200000000000000000000000000000000
χ402-2-2-22-22222-22-2-2-222-2-22-222-2-22222-22-2-2-2-22-22-220000-2-222-2-22200000000000000000000000000000000
χ412-2-2-22-2222-22-2222-2-2-2-22-222-2-22-2-2-22-22220000-2200000000000000000000000000000000002-2-22000000
χ422-2-2-22-2222-22-2222-2-2-2-22-222-2-22-2-2-22-22220000-220000000000000000000000000000000000-222-2000000
χ432-2-2-22-2222-22-22-2-222-2-22-222-22-222-22-22-2-22-2-222-2000022-2-2-2-22200000000000000000000000000000000
χ442-2-2-22-2222-22-22-2-222-2-22-222-22-222-22-22-2-2-222-22-20000-2-22222-2-200000000000000000000000000000000
χ452-2-2-22-222-12-22-2-2-22211-11-1-11-22-1-1-11-11112-22-21-10000-1-111-1-1113−33−33−33−300000000003−33−30000000000
χ462-2-2-22-222-12-22-2-2-22211-11-1-11-22-1-1-11-11112-22-21-10000-1-111-1-111−33−33−33−330000000000−33−330000000000
χ472-2-2-22-222-12-22-2-2-22211-11-1-11-22-1-1-11-1111-22-221-1000011-1-111-1-13−33−33−33−30000000000−33−330000000000
χ482-2-2-22-222-12-22-2-2-22211-11-1-11-22-1-1-11-1111-22-221-1000011-1-111-1-1−33−33−33−3300000000003−33−30000000000
χ492-2-2-22-222-1-22-22-2-22211-11-1-112-2-1-11-11-1112-2-22-110000-1-11111-1-13−33−3−33−3300000000003−3−330000000000
χ502-2-2-22-222-1-22-22-2-22211-11-1-112-2-1-11-11-1112-2-22-110000-1-11111-1-1−33−333−33−30000000000−333−30000000000
χ512-2-2-22-222-1-22-22-2-22211-11-1-112-2-1-11-11-111-222-2-11000011-1-1-1-1113−33−3−33−330000000000−333−30000000000
χ522-2-2-22-222-1-22-22-2-22211-11-1-112-2-1-11-11-111-222-2-11000011-1-1-1-111−33−333−33−300000000003−3−330000000000
χ5344444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200002200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000-2-200000000000000000000000000000000000000000000
χ55444-4-4-4-4440000000044-4-44-4-4000000000000000000000000000000000000004i−4i00000000000000000000
χ56444-4-4-4-4440000000044-4-44-4-400000000000000000000000000000000000000−4i4i00000000000000000000
χ5744-44-4-44-4-24i4i−4i−4i0000-22-2-22220000−2i−2i2i2i0000000022−22−2i22i200000000−2−222i2i2−i2−i2000000000000000000000000
χ5844-44-4-44-4-24i4i−4i−4i0000-22-2-22220000−2i−2i2i2i00000000−22222i2−2i20000000022−2−2−i2−i2i2i2000000000000000000000000
χ5944-44-4-44-4-2−4i−4i4i4i0000-22-2-222200002i2i−2i−2i0000000022−222i2−2i200000000−2−222−i2−i2i2i2000000000000000000000000
χ6044-44-4-44-4-2−4i−4i4i4i0000-22-2-222200002i2i−2i−2i00000000−2222−2i22i20000000022−2−2i2i2−i2−i2000000000000000000000000
χ6144-4-444-4-4400004-44-44-4-4-4-444004-400004-400000000000000000000000000000000000000000000000000
χ6244-4-444-4-440000-44-444-4-4-4-44400-440000-4400000000000000000000000000000000000000000000000000
χ6344-4-444-4-4-200004-44-4-22222-2-200-220000-22000000000023−2323−23000000000000000000000000000000000000
χ6444-4-444-4-4-200004-44-4-22222-2-200-220000-220000000000−2323−2323000000000000000000000000000000000000
χ6544-4-444-4-4-20000-44-44-22222-2-2002-200002-20000000000000023−2323−2300000000000000000000000000000000
χ6644-4-444-4-4-20000-44-44-22222-2-2002-200002-200000000000000−2323−232300000000000000000000000000000000
χ674-4444-4-4-4400004-4-44-44-44-44-400-4400004-400000000000000000000000000000000000000000000000000
χ684-4444-4-4-440000-444-4-44-44-44-4004-40000-4400000000000000000000000000000000000000000000000000
χ694-4444-4-4-4-200004-4-442-22-22-22002-20000-220000000000000023−23−232300000000000000000000000000000000
χ704-4444-4-4-4-200004-4-442-22-22-22002-20000-2200000000000000−232323−2300000000000000000000000000000000
χ714-4444-4-4-4-20000-444-42-22-22-2200-2200002-2000000000023−23−2323000000000000000000000000000000000000
χ724-4444-4-4-4-20000-444-42-22-22-2200-2200002-20000000000−232323−23000000000000000000000000000000000000
χ734-44-4-444-444i−4i−4i4i0000-444-4-4-4400004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ744-44-4-444-44−4i4i4i−4i0000-444-4-4-440000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ754-44-4-444-4-24i−4i−4i4i00002-2-2222-20000−2i2i2i−2i000000000000000000006−6−66−i6i6i6−i6000000000000000000000000
χ764-44-4-444-4-24i−4i−4i4i00002-2-2222-20000−2i2i2i−2i00000000000000000000−666−6i6−i6−i6i6000000000000000000000000
χ774-44-4-444-4-2−4i4i4i−4i00002-2-2222-200002i−2i−2i2i000000000000000000006−6−66i6−i6−i6i6000000000000000000000000
χ784-44-4-444-4-2−4i4i4i−4i00002-2-2222-200002i−2i−2i2i00000000000000000000−666−6−i6i6i6−i6000000000000000000000000
χ794-4-44-44-44400000000-4-4-444-4400000000000000000000000000000000000000004-4000000000000000000
χ804-4-44-44-44400000000-4-4-444-440000000000000000000000000000000000000000-44000000000000000000
χ814-4-4-44-444-24-44-444-4-422-22-2-224-422-22-22-2-20000-2200000000000000000000000000000000000000000000
χ824-4-4-44-444-2-44-4444-4-422-22-2-22-44222-22-2-2-200002-200000000000000000000000000000000000000000000
χ83888-8-8-8-88-400000000-4-444-444000000000000000000000000000000000000000000000000000000000000
χ848-8-88-88-88-400000000444-4-44-4000000000000000000000000000000000000000000000000000000000000

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