Finite Group Databasebeta

← Group #10848670

Character table — Group #10848670

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222224444444444444444444444444488888888888888888888888888888888242424242424242448484848
order12222234444666444444446612121212121212121212121212121212222444444466666612121212121212121212121212121212444488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111111111111111-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111-1-1-1-111111111111111-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ8111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ911111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ1311111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-111-1
χ1611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-11-1-11
χ172222222-2-2-2-2222000022-2-222-2-2-2-20000000022-2-202-2000002-20022-2-22-200000022-2-20000000000000000
χ182222222-2-2-2-2222000022-2-222-2-2-2-20000000022-2-20-2200000-2200-2-2222-2000000-2-2220000000000000000
χ192222222-2-2-2-22220000-2-22222-2-2-2-200000000-2-22202-200000-220022-2-2-22000000-2-2220000000000000000
χ202222222-2-2-2-22220000-2-22222-2-2-2-200000000-2-2220-22000002-200-2-222-2200000022-2-20000000000000000
χ21222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-2-2-22-2-2-1-11111-1-1-1-1111111111111000000000000
χ23222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-22222-2-2-2-2-211-1-1-1-11111-1-1-1-111111111000000000000
χ24222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-2-222-22211111111111111-1-1-1-1-1-1-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-111111111-1-1-1-1-222-2-2-2-2-22211-1-1-1-1-1-1111111-1-1-1-11111000000000000
χ26222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-111111111-1-1-1-1-2-2-22222-2-2-2111111-1-111-1-1-1-11111-1-1-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1111111111111222-2-2222-2-2-1-1-1-1-1-111-1-111111111-1-1-1-1000000000000
χ28222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111112-2-222-2-2222-1-1111111-1-1-1-1-1-1-1-1-1-11111000000000000
χ29222222-1-2-2-2-2-1-1-1000022-2-2-1-11111−i3−i3−i3−i3i3i3i3i3-1-11102-2000002-2−i3i3-1-111-11−i3i3−i3−i3i3i3-1-111−i3−i3i3i3000000000000
χ30222222-1-2-2-2-2-1-1-1000022-2-2-1-11111−i3−i3−i3−i3i3i3i3i3-1-1110-2200000-22−i3i311-1-1-11−i3i3i3i3−i3−i311-1-1i3i3−i3−i3000000000000
χ31222222-1-2-2-2-2-1-1-1000022-2-2-1-11111i3i3i3i3−i3−i3−i3−i3-1-11102-2000002-2i3−i3-1-111-11i3−i3i3i3−i3−i3-1-111i3i3−i3−i3000000000000
χ32222222-1-2-2-2-2-1-1-1000022-2-2-1-11111i3i3i3i3−i3−i3−i3−i3-1-1110-2200000-22i3−i311-1-1-11i3−i3−i3−i3i3i311-1-1−i3−i3i3i3000000000000
χ33222222-1-2-2-2-2-1-1-10000-2-222-1-11111−i3−i3−i3−i3i3i3i3i311-1-102-200000-22i3−i3-1-1111-1i3−i3−i3−i3i3i311-1-1i3i3−i3−i3000000000000
χ34222222-1-2-2-2-2-1-1-10000-2-222-1-11111−i3−i3−i3−i3i3i3i3i311-1-10-22000002-2i3−i311-1-11-1i3−i3i3i3−i3−i3-1-111−i3−i3i3i3000000000000
χ35222222-1-2-2-2-2-1-1-10000-2-222-1-11111i3i3i3i3−i3−i3−i3−i311-1-102-200000-22−i3i3-1-1111-1−i3i3i3i3−i3−i311-1-1−i3−i3i3i3000000000000
χ36222222-1-2-2-2-2-1-1-10000-2-222-1-11111i3i3i3i3−i3−i3−i3−i311-1-10-22000002-2−i3i311-1-11-1−i3i3−i3−i3i3i3-1-111i3i3−i3−i3000000000000
χ372222-2-222-2-2222222-2-22-22-2-2-222-2-222-2-222-2-222-2-22000000-200220000-22-2-2000000000000000000000000
χ382222-2-222-2-2222222-2-2-22-22-2-222-2-222-2-222-2-2-2-222-2000000200-2-200002-222000000000000000000000000
χ392222-2-222-2-22222-2-2222-22-2-2-222-2-2-2-222-2-22222-2-2-2000000200-2-20000-2222000000000000000000000000
χ402222-2-222-2-22222-2-222-22-22-2-222-2-2-2-222-2-222-2-2222000000-2002200002-2-2-2000000000000000000000000
χ412222-2-22-222-222200002-2-22-2-2-2-2220000000022220002-22-2000000000-2-2002-22-200002-22-2000000000000
χ422222-2-22-222-222200002-2-22-2-2-2-222000000002222000-22-22000000000-2-200-22-220000-22-22000000000000
χ432222-2-22-222-22220000-222-2-2-2-2-22200000000-2-2-2-20002-2-2200000000022002-22-20000-22-22000000000000
χ442222-2-22-222-22220000-222-2-2-2-2-22200000000-2-2-2-2000-222-20000000002200-22-2200002-22-2000000000000
χ452222-2-2-12-2-22-1-1-122-2-22-22-211-1-111-1-111-1-111-1-1112000000-200-1-1−i3i3−i3i31-111−i3i3i3−i3−i3i3−i3i3−i3i3i3−i3000000000000
χ462222-2-2-12-2-22-1-1-122-2-22-22-211-1-111-1-111-1-111-1-1112000000-200-1-1i3−i3i3−i31-111i3−i3−i3i3i3−i3i3−i3i3−i3−i3i3000000000000
χ472222-2-2-12-2-22-1-1-122-2-2-22-2211-1-111-1-111-1-11111-1-1-200000020011−i3i3−i3i3-11-1-1−i3i3i3−i3i3−i3i3−i3i3−i3−i3i3000000000000
χ482222-2-2-12-2-22-1-1-122-2-2-22-2211-1-111-1-111-1-11111-1-1-200000020011i3−i3i3−i3-11-1-1i3−i3−i3i3−i3i3−i3i3−i3i3i3−i3000000000000
χ492222-2-2-12-2-22-1-1-1-2-2222-22-211-1-11111-1-111-1-1-1-111-200000020011−i3i3−i3i31-1-1-1i3−i3−i3i3−i3i3−i3i3i3−i3−i3i3000000000000
χ502222-2-2-12-2-22-1-1-1-2-2222-22-211-1-11111-1-111-1-1-1-111-200000020011i3−i3i3−i31-1-1-1−i3i3i3−i3i3−i3i3−i3−i3i3i3−i3000000000000
χ512222-2-2-12-2-22-1-1-1-2-222-22-2211-1-11111-1-111-1-111-1-12000000-200-1-1−i3i3−i3i3-1111i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3000000000000
χ522222-2-2-12-2-22-1-1-1-2-222-22-2211-1-11111-1-111-1-111-1-12000000-200-1-1i3−i3i3−i3-1111−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3000000000000
χ532222-2-2-1-222-2-1-1-100002-2-221111-1-1−i3−i3i3i3i3i3−i3−i3-1-1-1-10002-22-2000−i3i3−i3i3i3−i311i3−i3-11-11−i3i3i3−i3-11-11000000000000
χ542222-2-2-1-222-2-1-1-100002-2-221111-1-1−i3−i3i3i3i3i3−i3−i3-1-1-1-1000-22-22000−i3i3i3−i3−i3i311i3−i31-11-1i3−i3−i3i31-11-1000000000000
χ552222-2-2-1-222-2-1-1-100002-2-221111-1-1i3i3−i3−i3−i3−i3i3i3-1-1-1-10002-22-2000i3−i3i3−i3−i3i311−i3i3-11-11i3−i3−i3i3-11-11000000000000
χ562222-2-2-1-222-2-1-1-100002-2-221111-1-1i3i3−i3−i3−i3−i3i3i3-1-1-1-1000-22-22000i3−i3−i3i3i3−i311−i3i31-11-1−i3i3i3−i31-11-1000000000000
χ572222-2-2-1-222-2-1-1-10000-222-21111-1-1−i3−i3i3i3i3i3−i3−i311110002-2-22000i3−i3−i3i3i3−i3-1-1−i3i3-11-11i3−i3−i3i31-11-1000000000000
χ582222-2-2-1-222-2-1-1-10000-222-21111-1-1−i3−i3i3i3i3i3−i3−i31111000-222-2000i3−i3i3−i3−i3i3-1-1−i3i31-11-1−i3i3i3−i3-11-11000000000000
χ592222-2-2-1-222-2-1-1-10000-222-21111-1-1i3i3−i3−i3−i3−i3i3i311110002-2-22000−i3i3i3−i3−i3i3-1-1i3−i3-11-11−i3i3i3−i31-11-1000000000000
χ602222-2-2-1-222-2-1-1-10000-222-21111-1-1i3i3−i3−i3−i3−i3i3i31111000-222-2000−i3i3−i3i3i3−i3-1-1i3−i31-11-1i3−i3−i3i3-11-11000000000000
χ612-2-222-2222-2-22-2-22i−2i2i−2i00002-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000002-2002i−2i0000
χ622-2-222-2222-2-22-2-22i−2i2i−2i00002-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000-2200−2i2i0000
χ632-2-222-2222-2-22-2-2−2i2i−2i2i00002-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000002-200−2i2i0000
χ642-2-222-2222-2-22-2-2−2i2i−2i2i00002-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000-22002i−2i0000
χ652-2-22-2222-22-22-2-22i−2i−2i2i0000-222-2-222i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000002-2002i−2i000000
χ662-2-22-2222-22-22-2-22i−2i−2i2i0000-222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000-2200−2i2i000000
χ672-2-22-2222-22-22-2-2−2i2i2i−2i0000-222-2-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000002-200−2i2i000000
χ682-2-22-2222-22-22-2-2−2i2i2i−2i0000-222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000-22002i−2i000000
χ694-4-444-44-4-4444-4-4000000004-4-44-4400000000000000000000000000000000000000000000000000000000
χ704-4-444-4-244-4-4-2224i−4i4i−4i0000-22-22-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ714-4-444-4-244-4-4-222−4i4i−4i4i0000-22-22-222i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ724-4-444-4-2-4-444-22200000000-222-22-223−2323−23−2323−2323000000000000000000000000000000000000000000000000
χ734-4-444-4-2-4-444-22200000000-222-22-2−2323−232323−2323−23000000000000000000000000000000000000000000000000
χ744-4-44-444-44-444-4-400000000-44-444-400000000000000000000000000000000000000000000000000000000
χ754-4-44-44-24-44-4-2224i−4i−4i4i00002-2-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ764-4-44-44-24-44-4-222−4i4i4i−4i00002-2-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000
χ774-4-44-44-2-44-44-222000000002-22-2-2223−23−2323−232323−23000000000000000000000000000000000000000000000000
χ784-4-44-44-2-44-44-222000000002-22-2-22−232323−2323−23−2323000000000000000000000000000000000000000000000000
χ7988-8-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-400004-4400000000000000000000000043−4300000000000000000000000000000000000000000000
χ8188-8-800-400004-44000000000000000000000000−434300000000000000000000000000000000000000000000
χ828-88-80080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ838-88-800-4000044-4000000000000000000000043−430000000000000000000000000000000000000000000000
χ848-88-800-4000044-40000000000000000000000−43430000000000000000000000000000000000000000000000

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