Finite Group Databasebeta

← Group #10894955

Character table — Group #10894955

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order1222222234444666666644448888888812121212121212121212121224242424242424242424242424242424224444444466121212121212444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1111111-1-1
χ911111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111111-111-1-1-1-111-1-1-1-11111-1-11-1
χ1011111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-1-1-1-1111111-1-1-1-111-11
χ1111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-11-1-11111-1-1-111-1-1-111-1-1-11
χ1211111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-11111-1-11-1-1111-1-1111-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1111-1-111-1-1-1-1-1-111-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1111-1-111-1-11111-1-111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111111-1-1-111-1-111-111-1-1-1-1-1111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-1-111-1-1111-1-111111-1-1-11
χ17222222222-2-2-2-2222222222-2-200000000-2-2-2-2-2-22222-2-20000000000000000000022-2-20000000000-200200000000
χ18222222222-2-2-2-2222222222-2-200000000-2-2-2-2-2-22222-2-200000000000000000000-2-2220000000000200-200000000
χ19222222222-2-2-2-22222222-2-22200000000-2-22222-2-2-2-2-2-20000000000000000000022-2-20000000000200-200000000
χ20222222222-2-2-2-22222222-2-22200000000-2-22222-2-2-2-2-2-200000000000000000000-2-2220000000000-200200000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211111111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122220000-2-2-1-1-1-11111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-20000221111-1-1-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-200002-2-1-11111-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-2220000-2211-1-1-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-122-2-20000-22-1-111-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-1-2-22200002-211-1-111-1-1000000000000
χ2922-2-22-22-222-22-22-22-22-2-2000000002i2i−2i−2i2-2000000002-2000000002i2i2i2i−2i−2i−2i−2i00002-22-20000000000000000002i−2i00
χ3022-2-22-22-222-22-22-22-22-2-2000000002i2i−2i−2i2-2000000002-2000000002i2i2i2i−2i−2i−2i−2i0000-22-22000000000000000000−2i2i00
χ3122-2-22-22-222-22-22-22-22-2-200000000−2i−2i2i2i2-2000000002-200000000−2i−2i−2i−2i2i2i2i2i00002-22-2000000000000000000−2i2i00
χ3222-2-22-22-222-22-22-22-22-2-200000000−2i−2i2i2i2-2000000002-200000000−2i−2i−2i−2i2i2i2i2i0000-22-220000000000000000002i−2i00
χ3322-2-22-22-22-22-222-22-22-2-200002i2i−2i−2i0000-2200000000-222i2i2i2i−2i−2i−2i−2i0000000000002-2-2200000000000000002i−2i0000
χ3422-2-22-22-22-22-222-22-22-2-200002i2i−2i−2i0000-2200000000-222i2i2i2i−2i−2i−2i−2i000000000000-222-20000000000000000−2i2i0000
χ3522-2-22-22-22-22-222-22-22-2-20000−2i−2i2i2i0000-2200000000-22−2i−2i−2i−2i2i2i2i2i0000000000002-2-220000000000000000−2i2i0000
χ3622-2-22-22-22-22-222-22-22-2-20000−2i−2i2i2i0000-2200000000-22−2i−2i−2i−2i2i2i2i2i000000000000-222-200000000000000002i−2i0000
χ372-22-22-2-2222-2-22-222-2-22-22i−2i2i−2i000000002-22i2i−2i−2i2i2i−2i−2i-2200000000000000002-22i−2i0000002-22i−2i0000000000000000
χ382-22-22-2-2222-2-22-222-2-22-22i−2i2i−2i000000002-22i2i−2i−2i2i2i−2i−2i-220000000000000000-22−2i2i000000-22−2i2i0000000000000000
χ392-22-22-2-2222-2-22-222-2-22-2−2i2i−2i2i000000002-2−2i−2i2i2i−2i−2i2i2i-2200000000000000002-2−2i2i0000002-2−2i2i0000000000000000
χ402-22-22-2-2222-2-22-222-2-22-2−2i2i−2i2i000000002-2−2i−2i2i2i−2i−2i2i2i-220000000000000000-222i−2i000000-222i−2i0000000000000000
χ412-22-22-2-222-222-2-222-2-22-22i−2i−2i2i00000000-22−2i−2i2i2i2i2i−2i−2i2-2000000000000000000000000000000000002-202i−2i000000
χ422-22-22-2-222-222-2-222-2-22-22i−2i−2i2i00000000-22−2i−2i2i2i2i2i−2i−2i2-200000000000000000000000000000000000-220−2i2i000000
χ432-22-22-2-222-222-2-222-2-22-2−2i2i2i−2i00000000-222i2i−2i−2i−2i−2i2i2i2-2000000000000000000000000000000000002-20−2i2i000000
χ442-22-22-2-222-222-2-222-2-22-2−2i2i2i−2i00000000-222i2i−2i−2i−2i−2i2i2i2-200000000000000000000000000000000000-2202i−2i000000
χ452-22-22-2-22-12-2-221-1-111-112i−2i2i−2i00000000-11−i−iii−i−iii1-133−3−333−3−3−i3−i3i3i3−i3−i3i3i32-22i−2i000000-11−ii−i3i33−3000000000000
χ462-22-22-2-22-12-2-221-1-111-112i−2i2i−2i00000000-11−i−iii−i−iii1-133−3−333−3−3−i3−i3i3i3−i3−i3i3i3-22−2i2i0000001-1i−ii3−i3−33000000000000
χ472-22-22-2-22-12-2-221-1-111-112i−2i2i−2i00000000-11−i−iii−i−iii1-1−3−333−3−333i3i3−i3−i3i3i3−i3−i32-22i−2i000000-11−iii3−i3−33000000000000
χ482-22-22-2-22-12-2-221-1-111-112i−2i2i−2i00000000-11−i−iii−i−iii1-1−3−333−3−333i3i3−i3−i3i3i3−i3−i3-22−2i2i0000001-1i−i−i3i33−3000000000000
χ492-22-22-2-22-12-2-221-1-111-11−2i2i−2i2i00000000-11ii−i−iii−i−i1-133−3−333−3−3i3i3−i3−i3i3i3−i3−i32-2−2i2i000000-11i−ii3−i33−3000000000000
χ502-22-22-2-22-12-2-221-1-111-11−2i2i−2i2i00000000-11ii−i−iii−i−i1-133−3−333−3−3i3i3−i3−i3i3i3−i3−i3-222i−2i0000001-1−ii−i3i3−33000000000000
χ512-22-22-2-22-12-2-221-1-111-11−2i2i−2i2i00000000-11ii−i−iii−i−i1-1−3−333−3−333−i3−i3i3i3−i3−i3i3i32-2−2i2i000000-11i−i−i3i3−33000000000000
χ522-22-22-2-22-12-2-221-1-111-11−2i2i−2i2i00000000-11ii−i−iii−i−i1-1−3−333−3−333−i3−i3i3i3−i3−i3i3i3-222i−2i0000001-1−iii3−i33−3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-400000000222222-2-2-2-2220000000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4440000000022-2-2-2-22222220000000000000000000000000000000000000000000000
χ554444-4-4-4-44000044-4-4-4-44000022−2222−22000000000000000022−2222−2222−2222−2200000000000000000000000000000000000000
χ564444-4-4-4-44000044-4-4-4-440000−2222−22220000000000000000−2222−2222−2222−222200000000000000000000000000000000000000
χ574444-4-4-4-4-20000-2-22222-2000022−2222−2200000023−2323−23000000−22−22−22−226−66−66−66−6000000000000000000000000000000
χ584444-4-4-4-4-20000-2-22222-2000022−2222−22000000−2323−2323000000−22−22−22−22−66−66−66−66000000000000000000000000000000
χ594444-4-4-4-4-20000-2-22222-20000−2222−222200000023−2323−230000002−22−22−22−2−66−66−66−66000000000000000000000000000000
χ604444-4-4-4-4-20000-2-22222-20000−2222−2222000000−2323−23230000002−22−22−22−26−66−66−66−6000000000000000000000000000000
χ6144-4-44-44-4-24-44-4-22-22-222000000004i4i−4i−4i-2200000000-2200000000−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000
χ6244-4-44-44-4-24-44-4-22-22-22200000000−4i−4i4i4i-2200000000-22000000002i2i2i2i−2i−2i−2i−2i000000000000000000000000000000
χ6344-4-44-44-4-2-44-44-22-22-22200004i4i−4i−4i00002-2000000002-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000
χ6444-4-44-44-4-2-44-44-22-22-2220000−4i−4i4i4i00002-2000000002-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000
χ6544-4-4-44-44400004-4-44-44-40000−2i22i22i2−2i20000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ6644-4-4-44-44400004-4-44-44-400002i2−2i2−2i22i200000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ6744-4-4-44-44-20000-222-22-220000−2i22i22i2−2i2000000000023−2323−2300i2−i2i2−i2−i2i2−i2i2i6−i6i6−i6−i6i6−i6i6000000000000000000000000000000
χ6844-4-4-44-44-20000-222-22-220000−2i22i22i2−2i20000000000−2323−232300i2−i2i2−i2−i2i2−i2i2−i6i6−i6i6i6−i6i6−i6000000000000000000000000000000
χ6944-4-4-44-44-20000-222-22-2200002i2−2i2−2i22i2000000000023−2323−2300−i2i2−i2i2i2−i2i2−i2−i6i6−i6i6i6−i6i6−i6000000000000000000000000000000
χ7044-4-4-44-44-20000-222-22-2200002i2−2i2−2i22i20000000000−2323−232300−i2i2−i2i2i2−i2i2−i2i6−i6i6−i6−i6i6−i6i6000000000000000000000000000000
χ714-44-44-4-44-2-444-42-2-222-224i−4i−4i4i000000002-22i2i−2i−2i−2i−2i2i2i-220000000000000000000000000000000000000000000000
χ724-44-44-4-44-2-444-42-2-222-22−4i4i4i−4i000000002-2−2i−2i2i2i2i2i−2i−2i-220000000000000000000000000000000000000000000000
χ734-44-4-444-440000-44-444-4-400000000−2i22i2−2i22i200000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ744-44-4-444-440000-44-444-4-4000000002i2−2i22i2−2i2000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ754-44-4-444-4-200002-22-2-22200000000−2i22i2−2i22i200−2i32i32i3−2i30000006−6−666−6−66i2−i2−i2i2i2−i2−i2i2000000000000000000000000000000
χ764-44-4-444-4-200002-22-2-22200000000−2i22i2−2i22i2002i3−2i3−2i32i3000000−666−6−666−6i2−i2−i2i2i2−i2−i2i2000000000000000000000000000000
χ774-44-4-444-4-200002-22-2-222000000002i2−2i22i2−2i200−2i32i32i3−2i3000000−666−6−666−6−i2i2i2−i2−i2i2i2−i2000000000000000000000000000000
χ784-44-4-444-4-200002-22-2-222000000002i2−2i22i2−2i2002i3−2i3−2i32i30000006−6−666−6−66−i2i2i2−i2−i2i2i2−i2000000000000000000000000000000
χ794-4-4444-4-4444-4-4-4-444-4-440000000000004400000000-4-40000000000000000000000000000000000000000000000
χ804-4-4444-4-44-4-444-4-444-4-44000000000000-4-400000000440000000000000000000000000000000000000000000000
χ814-4-4444-4-4-244-4-422-2-222-2000000000000-2-20000000022000000002323−23−23−23−232323000000000000000000000000000000
χ824-4-4444-4-4-244-4-422-2-222-2000000000000-2-2000000002200000000−23−2323232323−23−23000000000000000000000000000000
χ834-4-4444-4-4-2-4-44422-2-222-20000000000002200000000-2-2−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000000000
χ844-4-4444-4-4-2-4-44422-2-222-20000000000002200000000-2-22i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000000000
χ854-4-44-4-44440000-4-4-4-44440000000022−22−22220000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ864-4-44-4-44440000-4-4-4-444400000000−222222−2200000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ874-4-44-4-444-200002222-2-2-20000000022−22−2222000000−2i32i32i3−2i300−i6i6i6−i6i6−i6−i6i6−222−22−2−22000000000000000000000000000000
χ884-4-44-4-444-200002222-2-2-20000000022−22−22220000002i3−2i3−2i32i300i6−i6−i6i6−i6i6i6−i6−222−22−2−22000000000000000000000000000000
χ894-4-44-4-444-200002222-2-2-200000000−222222−22000000−2i32i32i3−2i300i6−i6−i6i6−i6i6i6−i62−2−22−222−2000000000000000000000000000000
χ904-4-44-4-444-200002222-2-2-200000000−222222−220000002i3−2i3−2i32i300−i6i6i6−i6i6−i6−i6i62−2−22−222−2000000000000000000000000000000

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