Finite Group Databasebeta

← Group #10848796

Character table — Group #10848796

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444466666664444888812121212121212122244666688121212121212242424242424242444448888246612122224448824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-11-1-11-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111
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
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-11-1-1-1-111
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-11111-1-1
χ911111111111111111111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-111-1-1-111-1-1-1-1-11-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-111111-11
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-11-1-111-1-1-1-111-1-1-11
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1111-1
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-111-1-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111-1-1111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11-111-1-1-1-1-1-111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111-111-1-11111-1-1-1-1-11
χ17222222222-2-2-2-2222222222-2-20000-2-22222-2-20000000000-2-200000000000022-2-20000000000-2002000000
χ18222222222-2-2-2-2222222222-2-20000-2-22222-2-20000000000-2-2000000000000-2-2220000000000200-2000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-200000000002200000000000022-2-20000000000200-2000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-2-2-2-2-2-2000000000022000000000000-2-2220000000000-2002000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-122-2-2-1-1-1-1-2-2111111-1-1-1-11111000000002-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-1-2-2221111-2-211-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-122-2-2-1-1-1-1221111111111-1-1-1-100000000-2211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1-2-22211112211-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ29222-22-2-2-222-22-222-22-2-2-22i−2i2i−2i00002-22i2i−2i−2i2-200000000002i−2i000000000000000022-2-20000000000002i−2i00
χ30222-22-2-2-222-22-222-22-2-2-22i−2i2i−2i00002-22i2i−2i−2i2-200000000002i−2i0000000000000000-2-222000000000000−2i2i00
χ31222-22-2-2-222-22-222-22-2-2-2−2i2i−2i2i00002-2−2i−2i2i2i2-20000000000−2i2i000000000000000022-2-2000000000000−2i2i00
χ32222-22-2-2-222-22-222-22-2-2-2−2i2i−2i2i00002-2−2i−2i2i2i2-20000000000−2i2i0000000000000000-2-2220000000000002i−2i00
χ33222-22-2-2-22-22-2222-22-2-2-22i−2i−2i2i22-2-2-222i2i−2i−2i-22000000002i−2i−2i2i000022-2-22i2i−2i−2i000000000000000000000000
χ34222-22-2-2-22-22-2222-22-2-2-22i−2i−2i2i-2-222-222i2i−2i−2i-2200000000−2i2i−2i2i0000-2-222−2i−2i2i2i000000000000000000000000
χ35222-22-2-2-22-22-2222-22-2-2-2−2i2i2i−2i22-2-2-22−2i−2i2i2i-2200000000−2i2i2i−2i000022-2-2−2i−2i2i2i000000000000000000000000
χ36222-22-2-2-22-22-2222-22-2-2-2−2i2i2i−2i-2-222-22−2i−2i2i2i-22000000002i−2i2i−2i0000-2-2222i2i−2i−2i000000000000000000000000
χ37222-22-2-2-2-1-22-22-1-11-11112i−2i−2i2i22-2-21-1−i−iii1-10000−i3−i3i3i32i−2ii−i33−3−3-1-111−i−iii0000000000−i3i33−30000000000
χ38222-22-2-2-2-1-22-22-1-11-11112i−2i−2i2i22-2-21-1−i−iii1-10000i3i3−i3−i32i−2ii−i−3−333-1-111−i−iii0000000000i3−i3−330000000000
χ39222-22-2-2-2-1-22-22-1-11-11112i−2i−2i2i-2-2221-1−i−iii1-10000−i3−i3i3i3−2i2ii−i33−3−311-1-1ii−i−i0000000000i3−i3−330000000000
χ40222-22-2-2-2-1-22-22-1-11-11112i−2i−2i2i-2-2221-1−i−iii1-10000i3i3−i3−i3−2i2ii−i−3−33311-1-1ii−i−i0000000000−i3i33−30000000000
χ41222-22-2-2-2-1-22-22-1-11-1111−2i2i2i−2i22-2-21-1ii−i−i1-10000−i3−i3i3i3−2i2i−ii−3−333-1-111ii−i−i0000000000−i3i3−330000000000
χ42222-22-2-2-2-1-22-22-1-11-1111−2i2i2i−2i22-2-21-1ii−i−i1-10000i3i3−i3−i3−2i2i−ii33−3−3-1-111ii−i−i0000000000i3−i33−30000000000
χ43222-22-2-2-2-1-22-22-1-11-1111−2i2i2i−2i-2-2221-1ii−i−i1-10000−i3−i3i3i32i−2i−ii−3−33311-1-1−i−iii0000000000i3−i33−30000000000
χ44222-22-2-2-2-1-22-22-1-11-1111−2i2i2i−2i-2-2221-1ii−i−i1-10000i3i3−i3−i32i−2i−ii33−3−311-1-1−i−iii0000000000−i3i3−330000000000
χ452-2-2-222-2222-2-22-2-2-222-2200000000-2200002-2002-2000000002-22-2000000002-22-2000000000000002-20000
χ462-2-2-222-2222-2-22-2-2-222-2200000000-2200002-2002-2000000002-22-200000000-22-2200000000000000-220000
χ472-2-2-222-2222-2-22-2-2-222-2200000000-2200002-200-2200000000-22-22000000002-22-200000000000000-220000
χ482-2-2-222-2222-2-22-2-2-222-2200000000-2200002-200-2200000000-22-2200000000-22-22000000000000002-20000
χ492-2-2-222-222-222-2-2-2-222-22000000002-20000-222-2002-22-200000000000000002-2-22000000000002-20000000
χ502-2-2-222-222-222-2-2-2-222-22000000002-20000-222-2002-22-20000000000000000-222-200000000000-220000000
χ512-2-2-222-222-222-2-2-2-222-22000000002-20000-22-2200-22-2200000000000000002-2-2200000000000-220000000
χ522-2-2-222-222-222-2-2-2-222-22000000002-20000-22-2200-22-220000000000000000-222-2000000000002-20000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4000022-2-2-2-222000000000022000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4440000222222220000000000-2-2000000000000000000000000000000000000
χ55444-44-4-4-4-24-44-4-2-22-22224i−4i4i−4i0000-22−2i−2i2i2i-220000000000−2i2i000000000000000000000000000000000000
χ56444-44-4-4-4-24-44-4-2-22-2222−4i4i−4i4i0000-222i2i−2i−2i-2200000000002i−2i000000000000000000000000000000000000
χ5744-44-44-4-4400004-4-4-4-444000022−2222−2200000000000000000000000022−2222−220000000000000000000000000000
χ5844-44-44-4-4400004-4-4-4-4440000−2222−2222000000000000000000000000−2222−22220000000000000000000000000000
χ5944-44-44-4-4-20000-22222-2-2000022−2222−2200−2i32i3−2i32i3000000000000000000−22−22i6−i6i6−i6000000000000000000000000
χ6044-44-44-4-4-20000-22222-2-2000022−2222−22002i3−2i32i3−2i3000000000000000000−22−22−i6i6−i6i6000000000000000000000000
χ6144-44-44-4-4-20000-22222-2-20000−2222−222200−2i32i3−2i32i30000000000000000002−22−2−i6i6−i6i6000000000000000000000000
χ6244-44-44-4-4-20000-22222-2-20000−2222−2222002i3−2i32i3−2i30000000000000000002−22−2i6−i6i6−i6000000000000000000000000
χ6344-4-4-4-444400004-44-44-4-4000022−22−222200000000000000000000000022−22−22220000000000000000000000000000
χ6444-4-4-4-444400004-44-44-4-40000−222222−22000000000000000000000000−222222−220000000000000000000000000000
χ6544-4-4-4-444-20000-22-22-222000022−22−22220023−23−2323000000000000000000−222−2−666−6000000000000000000000000
χ6644-4-4-4-444-20000-22-22-222000022−22−222200−232323−23000000000000000000−222−26−6−66000000000000000000000000
χ6744-4-4-4-444-20000-22-22-2220000−222222−220023−23−23230000000000000000002−2−226−6−66000000000000000000000000
χ6844-4-4-4-444-20000-22-22-2220000−222222−2200−232323−230000000000000000002−2−22−666−6000000000000000000000000
χ694-444-4-4-4440000-44-4-444-40000000000000000000000000000000000000000000022−2222−220000000000000000
χ704-444-4-4-4440000-44-4-444-400000000000000000000000000000000000000000000−2222−22220000000000000000
χ714-44-4-444-440000-444-4-4-440000000000000000000000000000000000000000000022−22−22220000000000000000
χ724-44-4-444-440000-444-4-4-4400000000000000000000000000000000000000000000−222222−220000000000000000
χ734-4-444-44-4444-4-4-4-444-44-400000000-4-4000044000000000000000000000000000000000000000000000000
χ744-4-444-44-44-4-444-4-444-44-400000000440000-4-4000000000000000000000000000000000000000000000000
χ754-4-444-44-4-244-4-422-2-22-2200000000220000-2-20000−2i32i32i3−2i30000000000000000000000000000000000000000
χ764-4-444-44-4-244-4-422-2-22-2200000000220000-2-200002i3−2i3−2i32i30000000000000000000000000000000000000000
χ774-4-444-44-4-2-4-44422-2-22-2200000000-2-200002200000000000023−23−232300000000000000000000000000000000
χ784-4-444-44-4-2-4-44422-2-22-2200000000-2-2000022000000000000−232323−2300000000000000000000000000000000
χ794-4-4-444-44-24-4-44222-2-22-2000000002-20000-22004-400000000-22-2200000000000000000000000000000000
χ804-4-4-444-44-24-4-44222-2-22-2000000002-20000-2200-44000000002-22-200000000000000000000000000000000
χ814-4-4-444-44-2-444-4222-2-22-200000000-2200002-24-400-22-220000000000000000000000000000000000000000
χ824-4-4-444-44-2-444-4222-2-22-200000000-2200002-2-44002-22-20000000000000000000000000000000000000000
χ838-888-8-8-88-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-888-8-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000

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