Finite Group Databasebeta

← Group #10692500

Character table — Group #10692500

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order12222222223446662244444444466666612121212661212121212121212888888888888888844441212121212121212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ61111111111111111-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1
χ911111-1-1-1-111-1-111111-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i11-1-11-1
χ1011111-1-1-1-111-1-111111-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-1-111-11
χ1111111-1-1-1-111-1-111111-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-1-111-11
χ1211111-1-1-1-111-1-111111-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii11-1-11-1
χ1311111-1-1-1-111-1-1111-1-111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii11-1-1-11
χ1411111-1-1-1-111-1-1111-1-111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-1-1111-1
χ1511111-1-1-1-111-1-1111-1-111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-1-1111-1
χ1611111-1-1-1-111-1-1111-1-111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i11-1-1-11
χ1722222222222-2-22222222-2-2-2-2-2-2-2222222-2-2-2-222-2-222-2-2-2-20000000000000000000000000000000000
χ1822222222222-2-2222-2-2-2-222-2-2-222222222-2-2-2-2-2-222-2-2-2-2220000000000000000000000000000000000
χ192222222222-122-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ202222222222-122-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ212222222222-122-1-1-1-2-2-2-2-2-2222-2-2-1-1-1-1-1-1-1-1-1-1111111-1-111000000000000000022-2-2-1-1-1-11111000000
χ222222222222-122-1-1-1-2-2-2-2-2-2222-2-2-1-1-1-1-1-1-1-1-1-1111111-1-1110000000000000000-2-2221111-1-1-1-1000000
χ232222222222-1-2-2-1-1-12222-2-2-2-2-2-2-2-1-1-1-1-1-11111-1-111-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i3000000
χ242222222222-1-2-2-1-1-12222-2-2-2-2-2-2-2-1-1-1-1-1-11111-1-111-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i3000000
χ252222222222-1-2-2-1-1-1-2-2-2-222-2-2-222-1-1-1-1-1-1111111-1-11111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ262222222222-1-2-2-1-1-1-2-2-2-222-2-2-222-1-1-1-1-1-1111111-1-11111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ2722222-2-2-2-2222222222-2-2-2-2-2-222222-2-2-2-2222222-2-2-2-2-2-2220000000000000000000000000000000000
χ2822222-2-2-2-22222222-2-22222-2-22-2-222-2-2-2-22222-2-22222-2-2-2-20000000000000000000000000000000000
χ2922222-2-2-2-22-122-1-1-122-2-2-2-2-2-2222-1-11111-1-1-1-1-1-1111111-1-1000000000000000000003−3−333−3−33000000
χ3022222-2-2-2-22-122-1-1-122-2-2-2-2-2-2222-1-11111-1-1-1-1-1-1111111-1-100000000000000000000−333−3−333−3000000
χ3122222-2-2-2-22-122-1-1-1-2-22222-2-22-2-2-1-11111-1-1-1-111-1-1-1-11111000000000000000000003−3−33−333−3000000
χ3222222-2-2-2-22-122-1-1-1-2-22222-2-22-2-2-1-11111-1-1-1-111-1-1-1-1111100000000000000000000−333−33−3−33000000
χ3322222-2-2-2-22-1-2-2-1-1-122-2-22222-2-2-2-1-111111111-1-1-1-111-1-11100000000000000002i−2i2i−2i−i−iii−i−iii000000
χ3422222-2-2-2-22-1-2-2-1-1-122-2-22222-2-2-2-1-111111111-1-1-1-111-1-1110000000000000000−2i2i−2i2iii−i−iii−i−i000000
χ3522222-2-2-2-22-1-2-2-1-1-1-2-222-2-222-222-1-1111111111111-1-1-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i000000
χ3622222-2-2-2-22-1-2-2-1-1-1-2-222-2-222-222-1-1111111111111-1-1-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii000000
χ372222-22-22-2-22222220000002-2-200-2-22-22-222-2-20000002-2000000000022-2-222-2-2000000000000000000
χ382222-22-22-2-22222220000002-2-200-2-22-22-222-2-20000002-20000000000-2-222-2-222000000000000000000
χ392222-22-22-2-22-2-2222000000-22200-2-22-22-2-2-222000000-22002i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ402222-22-22-2-22-2-2222000000-22200-2-22-22-2-2-222000000-2200−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ412222-2-22-22-2222222000000-22-200-2-2-22-2222-2-2000000-220022-2-2-2-22200000000000000000000000000
χ422222-2-22-22-2222222000000-22-200-2-2-22-2222-2-2000000-2200-2-22222-2-200000000000000000000000000
χ432222-2-22-22-22-2-22220000002-2200-2-2-22-22-2-2220000002-200000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ442222-2-22-22-22-2-22220000002-2200-2-2-22-22-2-2220000002-20000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ4522-2-2222-2-2-22002-2-22-22-200000002-222-2-200002-2002-200002−22−22−22−22−22−22−22−2000000000000000000
χ4622-2-2222-2-2-22002-2-22-22-200000002-222-2-200002-2002-20000−22−22−22−22−22−22−22−22000000000000000000
χ4722-2-2222-2-2-22002-2-2-22-2200000002-222-2-20000-2200-2200002−22−22−22−2−22−22−22−22000000000000000000
χ4822-2-2222-2-2-22002-2-2-22-2200000002-222-2-20000-2200-220000−22−22−22−222−22−22−22−2000000000000000000
χ4922-2-22-2-222-22002-2-22-2-2200000002-2-2-22200002-200-220000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ5022-2-22-2-222-22002-2-22-2-2200000002-2-2-22200002-200-220000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ5122-2-22-2-222-22002-2-2-222-200000002-2-2-2220000-22002-20000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ5222-2-22-2-222-22002-2-2-222-200000002-2-2-2220000-22002-20000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ5322-2-2-22-2-2222002-2-200002i−2i0002i−2i-222-2-220000002i−2i00002i−2i−i2i2i2−i2−i2i2i2−i22−2−222−2−22000000000000000000
χ5422-2-2-22-2-2222002-2-200002i−2i0002i−2i-222-2-220000002i−2i00002i−2ii2−i2−i2i2i2−i2−i2i2−222−2−222−2000000000000000000
χ5522-2-2-22-2-2222002-2-20000−2i2i000−2i2i-222-2-22000000−2i2i0000−2i2i−i2i2i2−i2−i2i2i2−i2−222−2−222−2000000000000000000
χ5622-2-2-22-2-2222002-2-20000−2i2i000−2i2i-222-2-22000000−2i2i0000−2i2ii2−i2−i2i2i2−i2−i2i22−2−222−2−22000000000000000000
χ5722-2-2-2-222-222002-2-200002i−2i000−2i2i-22-222-20000002i−2i0000−2i2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i2000000000000000000
χ5822-2-2-2-222-222002-2-200002i−2i000−2i2i-22-222-20000002i−2i0000−2i2i−222−22−2−22−i2i2i2−i2i2−i2−i2i2000000000000000000
χ5922-2-2-2-222-222002-2-20000−2i2i0002i−2i-22-222-2000000−2i2i00002i−2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i2000000000000000000
χ6022-2-2-2-222-222002-2-20000−2i2i0002i−2i-22-222-2000000−2i2i00002i−2i−222−22−2−22i2−i2−i2i2−i2i2i2−i2000000000000000000
χ614444-44-44-4-4-244-2-2-20000004-4-40022-22-22-2-222000000-22000000000000000000000000000000000000
χ624444-44-44-4-4-2-4-4-2-2-2000000-4440022-22-2222-2-20000002-2000000000000000000000000000000000000
χ634444-4-44-44-4-244-2-2-2000000-44-400222-22-2-2-2220000002-2000000000000000000000000000000000000
χ644444-4-44-44-4-2-4-4-2-2-20000004-4400222-22-222-2-2000000-22000000000000000000000000000000000000
χ6544-4-4444-4-4-4-200-2224-44-40000000-22-2-2220000-2200-2200000000000000000000000000000000000000
χ6644-4-4444-4-4-4-200-222-44-440000000-22-2-22200002-2002-200000000000000000000000000000000000000
χ6744-4-44-4-444-4-200-2224-4-440000000-2222-2-20000-22002-200000000000000000000000000000000000000
χ6844-4-44-4-444-4-200-222-444-40000000-2222-2-200002-200-2200000000000000000000000000000000000000
χ6944-4-4-44-4-444-200-22200004i−4i0004i−4i2-2-222-2000000−2i2i0000−2i2i0000000000000000000000000000000000
χ7044-4-4-44-4-444-200-2220000−4i4i000−4i4i2-2-222-20000002i−2i00002i−2i0000000000000000000000000000000000
χ7144-4-4-4-444-44-200-22200004i−4i000−4i4i2-22-2-22000000−2i2i00002i−2i0000000000000000000000000000000000
χ7244-4-4-4-444-44-200-2220000−4i4i0004i−4i2-22-2-220000002i−2i0000−2i2i0000000000000000000000000000000000
χ734-44-400000044i−4i-44-4000000000000000004i−4i00000000000000000000000000000000000000002-22i−2i00
χ744-44-400000044i−4i-44-4000000000000000004i−4i0000000000000000000000000000000000000000-22−2i2i00
χ754-44-40000004−4i4i-44-400000000000000000−4i4i00000000000000000000000000000000000000002-2−2i2i00
χ764-44-40000004−4i4i-44-400000000000000000−4i4i0000000000000000000000000000000000000000-222i−2i00
χ778-88-8000000-48i−8i4-4400000000000000000−4i4i0000000000000000000000000000000000000000000000
χ788-88-8000000-4−8i8i4-44000000000000000004i−4i0000000000000000000000000000000000000000000000
χ798-8-88000000800-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-8-88000000-40044-40000000000000000000−4i34i300000000000000000000000000000000000000000000
χ818-8-88000000-40044-400000000000000000004i3−4i300000000000000000000000000000000000000000000

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