Finite Group Databasebeta

← Group #10848858

Character table — Group #10848858

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order122222223444466666664444888888881212121212121212121212122424242424242424242424242424242444444444441212121212121212222444888844
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
χ911111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111111-111-1-111-1-1-111-1-1-111-1-11-1
χ1011111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-1-111-1-11-1-1111-1-111-11
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-11-1-111-1-111-1-1-1-11111-1-1-11
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1-1111111-1-1-1-1111-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1111-1-1-1-111-111-1-1-1-1-111-11
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1111-1-1-1-1111-1-111111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111111-1-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-1-11111-1-11111-1-111-1-1-11
χ17222222222-2-2-2-2222222222-2-2000000002222-2-2-2-2-2-2-2-20000000000000000000022-2-20000000000-200200000000
χ18222222222-2-2-2-2222222222-2-2000000002222-2-2-2-2-2-2-2-200000000000000000000-2-2220000000000200-200000000
χ19222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-22222-2-20000000000000000000022-2-20000000000200-200000000
χ20222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-22222-2-200000000000000000000-2-2220000000000-200200000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-21111-1-11111-1-1-1-1-1-1-1-1-1-11111111122-2-200002-2-1-111-1-111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-21111-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-2220000-2211-1-111-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-20000-22-1-11111-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-22200002-211-1-1-1-111000000000000
χ29222-2-2-2-2222-22-222-2-2-22-2000000002i2i−2i−2i00002-200002-2000000002i2i2i2i−2i−2i−2i−2i00002i−2i2i−2i0000000000000000002-200
χ30222-2-2-2-2222-22-222-2-2-22-2000000002i2i−2i−2i00002-200002-2000000002i2i2i2i−2i−2i−2i−2i0000−2i2i−2i2i000000000000000000-2200
χ31222-2-2-2-2222-22-222-2-2-22-200000000−2i−2i2i2i00002-200002-200000000−2i−2i−2i−2i2i2i2i2i00002i−2i2i−2i000000000000000000-2200
χ32222-2-2-2-2222-22-222-2-2-22-200000000−2i−2i2i2i00002-200002-200000000−2i−2i−2i−2i2i2i2i2i0000−2i2i−2i2i0000000000000000002-200
χ33222-2-2-2-222-22-2222-2-2-22-200002i2i−2i−2i00000000-220000-222i2i2i2i−2i−2i−2i−2i0000000000002i−2i−2i2i00000000000000002-20000
χ34222-2-2-2-222-22-2222-2-2-22-200002i2i−2i−2i00000000-220000-222i2i2i2i−2i−2i−2i−2i000000000000−2i2i2i−2i0000000000000000-220000
χ35222-2-2-2-222-22-2222-2-2-22-20000−2i−2i2i2i00000000-220000-22−2i−2i−2i−2i2i2i2i2i0000000000002i−2i−2i2i0000000000000000-220000
χ36222-2-2-2-222-22-2222-2-2-22-20000−2i−2i2i2i00000000-220000-22−2i−2i−2i−2i2i2i2i2i000000000000−2i2i2i−2i00000000000000002-20000
χ372-2-22-2-222222-2-2-2-2-2-22222-22-20000000022-2-2-2-222-2-22200000000000000002-22-20000002-22-20000000000000000
χ382-2-22-2-222222-2-2-2-2-2-22222-22-20000000022-2-2-2-222-2-2220000000000000000-22-22000000-22-220000000000000000
χ392-2-22-2-222222-2-2-2-2-2-2222-22-2200000000-2-222-2-2-2-2222200000000000000002-2-220000002-2-220000000000000000
χ402-2-22-2-222222-2-2-2-2-2-2222-22-2200000000-2-222-2-2-2-222220000000000000000-222-2000000-222-20000000000000000
χ412-2-22-2-2222-2-222-2-2-2-22222-2-220000000022-2-222-2-222-2-2000000000000000000000000000000000002-202-2000000
χ422-2-22-2-2222-2-222-2-2-2-22222-2-220000000022-2-222-2-222-2-200000000000000000000000000000000000-220-22000000
χ432-2-22-2-2222-2-222-2-2-2-2222-222-200000000-2-2222222-2-2-2-2000000000000000000000000000000000002-20-22000000
χ442-2-22-2-2222-2-222-2-2-2-2222-222-200000000-2-2222222-2-2-2-200000000000000000000000000000000000-2202-2000000
χ452-2-22-2-222-122-2-21111-1-1-12-22-200000000-1-11111-1-111-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i32-22-2000000-11-11−i3i3−i3i3000000000000
χ462-2-22-2-222-122-2-21111-1-1-12-22-200000000-1-11111-1-111-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-22-220000001-11-1i3−i3i3−i3000000000000
χ472-2-22-2-222-122-2-21111-1-1-12-22-200000000-1-11111-1-111-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i32-22-2000000-11-11i3−i3i3−i3000000000000
χ482-2-22-2-222-122-2-21111-1-1-12-22-200000000-1-11111-1-111-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-22-220000001-11-1−i3i3−i3i3000000000000
χ492-2-22-2-222-122-2-21111-1-1-1-22-220000000011-1-11111-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i32-2-22000000-111-1−i3i3i3−i3000000000000
χ502-2-22-2-222-122-2-21111-1-1-1-22-220000000011-1-11111-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-222-20000001-1-11i3−i3−i3i3000000000000
χ512-2-22-2-222-122-2-21111-1-1-1-22-220000000011-1-11111-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i32-2-22000000-111-1i3−i3−i3i3000000000000
χ522-2-22-2-222-122-2-21111-1-1-1-22-220000000011-1-11111-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-222-20000001-1-11−i3i3i3−i3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-400000000-2-2-2-2222222220000000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44400000000222222-2-2-2-2220000000000000000000000000000000000000000000000
χ55444-4-4-4-44-24-44-4-2-2222-22000000004i4i−4i−4i0000-220000-2200000000−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000
χ56444-4-4-4-44-24-44-4-2-2222-2200000000−4i−4i4i4i0000-220000-22000000002i2i2i2i−2i−2i−2i−2i000000000000000000000000000000
χ57444-4-4-4-44-2-44-44-2-2222-2200004i4i−4i−4i000000002-200002-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000
χ58444-4-4-4-44-2-44-44-2-2222-220000−4i−4i4i4i000000002-200002-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000
χ5944-444-4-4-4400004-44-44-4-40000000022−2222−220000000000000000000022−2222−2222−2222−22000000000000000000000000000000
χ6044-444-4-4-4400004-44-44-4-400000000−2222−222200000000000000000000−2222−2222−2222−2222000000000000000000000000000000
χ6144-444-4-4-4-20000-22-22-2220000000022−2222−22−2i32i3−2i32i300000000i6−i6i6−i6i6−i6i6−i6−22−22−22−22000000000000000000000000000000
χ6244-444-4-4-4-20000-22-22-2220000000022−2222−222i3−2i32i3−2i300000000−i6i6−i6i6−i6i6−i6i6−22−22−22−22000000000000000000000000000000
χ6344-444-4-4-4-20000-22-22-22200000000−2222−2222−2i32i3−2i32i300000000−i6i6−i6i6−i6i6−i6i62−22−22−22−2000000000000000000000000000000
χ6444-444-4-4-4-20000-22-22-22200000000−2222−22222i3−2i32i3−2i300000000i6−i6i6−i6i6−i6i6−i62−22−22−22−2000000000000000000000000000000
χ6544-4-4-444-4400004-4-44-4-4400000000−2i22i22i2−2i200000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ6644-4-4-444-4400004-4-44-4-44000000002i2−2i2−2i22i2000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ6744-4-4-444-4-20000-222-222-200000000−2i22i22i2−2i2000000−2i32i3−2i32i3006−66−6−66−66i2−i2i2−i2−i2i2−i2i2000000000000000000000000000000
χ6844-4-4-444-4-20000-222-222-200000000−2i22i22i2−2i20000002i3−2i32i3−2i300−66−666−66−6i2−i2i2−i2−i2i2−i2i2000000000000000000000000000000
χ6944-4-4-444-4-20000-222-222-2000000002i2−2i2−2i22i2000000−2i32i3−2i32i300−66−666−66−6−i2i2−i2i2i2−i2i2−i2000000000000000000000000000000
χ7044-4-4-444-4-20000-222-222-2000000002i2−2i2−2i22i20000002i3−2i32i3−2i3006−66−6−66−66−i2i2−i2i2i2−i2i2−i2000000000000000000000000000000
χ714-444-44-4-440000-44-444-4-4000022−2222−22000000000000000022−22−222222−22−222200000000000000000000000000000000000000
χ724-444-44-4-440000-44-444-4-40000−2222−22220000000000000000−222222−22−222222−2200000000000000000000000000000000000000
χ734-444-44-4-4-200002-22-2-222000022−2222−220000−2i32i32i3−2i300000000−222−2−222−2i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000
χ744-444-44-4-4-200002-22-2-222000022−2222−2200002i3−2i3−2i32i300000000−222−2−222−2−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000
χ754-444-44-4-4-200002-22-2-2220000−2222−22220000−2i32i32i3−2i3000000002−2−222−2−22−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000
χ764-444-44-4-4-200002-22-2-2220000−2222−222200002i3−2i3−2i32i3000000002−2−222−2−22i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000
χ774-44-44-44-440000-444-4-4-440000−2i22i22i2−2i20000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ784-44-44-44-440000-444-4-4-4400002i2−2i2−2i22i200000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ794-44-44-44-4-200002-2-2222-20000−2i22i22i2−2i20000000000−2i32i32i3−2i300i2−i2−i2i2−i2i2i2−i26−6−66−666−6000000000000000000000000000000
χ804-44-44-44-4-200002-2-2222-20000−2i22i22i2−2i200000000002i3−2i3−2i32i300i2−i2−i2i2−i2i2i2−i2−666−66−6−66000000000000000000000000000000
χ814-44-44-44-4-200002-2-2222-200002i2−2i2−2i22i20000000000−2i32i32i3−2i300−i2i2i2−i2i2−i2−i2i2−666−66−6−66000000000000000000000000000000
χ824-44-44-44-4-200002-2-2222-200002i2−2i2−2i22i200000000002i3−2i3−2i32i300−i2i2i2−i2i2−i2−i2i26−6−66−666−6000000000000000000000000000000
χ834-4-44-4-444-2-4-4442222-2-2-24-4-4400000000-2-222-2-222-2-2220000000000000000000000000000000000000000000000
χ844-4-44-4-444-2-4-4442222-2-2-2-444-40000000022-2-2-2-2-2-222220000000000000000000000000000000000000000000000
χ854-4-4-444-4444-4-44-4-444-44-40000000000000000-4400004-40000000000000000000000000000000000000000000000
χ864-4-4-444-444-444-4-4-444-44-400000000000000004-40000-440000000000000000000000000000000000000000000000
χ874-4-4-444-44-24-4-4422-2-22-2200000000000000002-20000-22000000002323−23−23−23−232323000000000000000000000000000000
χ884-4-4-444-44-24-4-4422-2-22-2200000000000000002-20000-2200000000−23−2323232323−23−23000000000000000000000000000000
χ894-4-4-444-44-2-444-422-2-22-220000000000000000-2200002-22323−23−23−23−23232300000000000000000000000000000000000000
χ904-4-4-444-44-2-444-422-2-22-220000000000000000-2200002-2−23−2323232323−23−2300000000000000000000000000000000000000

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