Finite Group Databasebeta

← Group #10692959

Character table — Group #10692959

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
χ51111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ61111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1
χ911111-1-1-1-111-1-1111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i11-1-11-1
χ1011111-1-1-1-111-1-1111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-1-111-11
χ1111111-1-1-1-111-1-1111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-1-111-11
χ1211111-1-1-1-111-1-1111111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii11-1-11-1
χ1311111-1-1-1-111-1-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii11-1-1-11
χ1411111-1-1-1-111-1-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-1-1111-1
χ1511111-1-1-1-111-1-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-1-1111-1
χ1611111-1-1-1-111-1-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i11-1-1-11
χ1722222222222-2-222222-2-2-2-2-2-2-222222222-2-2-2-222-2-222-2-2-2-20000000000000000000000000000000000
χ1822222222222-2-2222-2-222-2-2-222-2-2222222-2-2-2-2-2-222-2-2-2-2220000000000000000000000000000000000
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
χ212222222222-122-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111-1-111000000000000000022-2-2-1-1-1-11111000000
χ222222222222-122-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111-1-1110000000000000000-2-2221111-1-1-1-1000000
χ232222222222-1-2-2-1-1-122-2-2-2-2-2-2-222-1-1-1-1-1-11111-1-111-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i3000000
χ242222222222-1-2-2-1-1-122-2-2-2-2-2-2-222-1-1-1-1-1-11111-1-111-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i3000000
χ252222222222-1-2-2-1-1-1-2-222-2-2-222-2-2-1-1-1-1-1-1111111-1-11111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i3000000
χ262222222222-1-2-2-1-1-1-2-222-2-2-222-2-2-1-1-1-1-1-1111111-1-11111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i3000000
χ2722222-2-2-2-2222222222-2-2-2-2222-2-222-2-2-2-2222222-2-2-2-2-2-2220000000000000000000000000000000000
χ2822222-2-2-2-22222222-2-222-2-22-2-22222-2-2-2-22222-2-22222-2-2-2-20000000000000000000000000000000000
χ2922222-2-2-2-22-122-1-1-122-2-2-2-2222-2-2-1-11111-1-1-1-1-1-1111111-1-1000000000000000000003−3−333−3−33000000
χ3022222-2-2-2-22-122-1-1-122-2-2-2-2222-2-2-1-11111-1-1-1-1-1-1111111-1-100000000000000000000−333−3−333−3000000
χ3122222-2-2-2-22-122-1-1-1-2-222-2-22-2-222-1-11111-1-1-1-111-1-1-1-11111000000000000000000003−3−33−333−3000000
χ3222222-2-2-2-22-122-1-1-1-2-222-2-22-2-222-1-11111-1-1-1-111-1-1-1-1111100000000000000000000−333−33−3−33000000
χ3322222-2-2-2-22-1-2-2-1-1-1222222-2-2-2-2-2-1-111111111-1-1-1-111-1-11100000000000000002i−2i2i−2i−i−iii−i−iii000000
χ3422222-2-2-2-22-1-2-2-1-1-1222222-2-2-2-2-2-1-111111111-1-1-1-111-1-1110000000000000000−2i2i−2i2iii−i−iii−i−i000000
χ3522222-2-2-2-22-1-2-2-1-1-1-2-2-2-222-22222-1-1111111111111-1-1-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i000000
χ3622222-2-2-2-22-1-2-2-1-1-1-2-2-2-222-22222-1-1111111111111-1-1-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii000000
χ372222-22-22-2-222222200002-2-20000-2-22-22-222-2-20000002-2000000000022-2-222-2-2000000000000000000
χ382222-22-22-2-222222200002-2-20000-2-22-22-222-2-20000002-20000000000-2-222-2-222000000000000000000
χ392222-22-22-2-22-2-22220000-2220000-2-22-22-2-2-222000000-22002i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ402222-22-22-2-22-2-22220000-2220000-2-22-22-2-2-222000000-2200−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ412222-2-22-22-22222220000-22-20000-2-2-22-2222-2-2000000-220022-2-2-2-22200000000000000000000000000
χ422222-2-22-22-22222220000-22-20000-2-2-22-2222-2-2000000-2200-2-22222-2-200000000000000000000000000
χ432222-2-22-22-22-2-222200002-220000-2-2-22-22-2-2220000002-200000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ442222-2-22-22-22-2-222200002-220000-2-2-22-22-2-2220000002-20000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ452-2-2222-2-22-22002-2-2002i−2i0002i−2i002-22-2-220000002i−2i00002i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000000000
χ462-2-2222-2-22-22002-2-2002i−2i0002i−2i002-22-2-220000002i−2i00002i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000000000
χ472-2-2222-2-22-22002-2-200−2i2i000−2i2i002-22-2-22000000−2i2i0000−2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000000000000000
χ482-2-2222-2-22-22002-2-200−2i2i000−2i2i002-22-2-22000000−2i2i0000−2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000000000
χ492-2-222-222-2-22002-2-2002i−2i000−2i2i002-2-222-20000002i−2i0000−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000000000
χ502-2-222-222-2-22002-2-2002i−2i000−2i2i002-2-222-20000002i−2i0000−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000000000
χ512-2-222-222-2-22002-2-200−2i2i0002i−2i002-2-222-2000000−2i2i00002i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000000000
χ522-2-222-222-2-22002-2-200−2i2i0002i−2i002-2-222-2000000−2i2i00002i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000000000
χ532-2-22-222-2-222002-2-22-200000002-2-2222-2-200002-2002-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ542-2-22-222-2-222002-2-22-200000002-2-2222-2-200002-2002-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ552-2-22-222-2-222002-2-2-220000000-22-2222-2-20000-2200-220000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ562-2-22-222-2-222002-2-2-220000000-22-2222-2-20000-2200-220000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ572-2-22-2-2-22222002-2-22-20000000-22-22-2-22200002-200-2200002−2−22−222−22−2−22−222−2000000000000000000
χ582-2-22-2-2-22222002-2-22-20000000-22-22-2-22200002-200-220000−222−22−2−22−222−22−2−22000000000000000000
χ592-2-22-2-2-22222002-2-2-2200000002-2-22-2-2220000-22002-200002−2−22−222−2−222−22−2−22000000000000000000
χ602-2-22-2-2-22222002-2-2-2200000002-2-22-2-2220000-22002-20000−222−22−2−222−2−22−222−2000000000000000000
χ614444-44-44-4-4-244-2-2-200004-4-4000022-22-22-2-222000000-22000000000000000000000000000000000000
χ624444-44-44-4-4-2-4-4-2-2-20000-444000022-22-2222-2-20000002-2000000000000000000000000000000000000
χ634444-4-44-44-4-244-2-2-20000-44-40000222-22-2-2-2220000002-2000000000000000000000000000000000000
χ644444-4-44-44-4-2-4-4-2-2-200004-440000222-22-222-2-2000000-22000000000000000000000000000000000000
χ654-44-400000044-4-4-44000000000000000004-400000000000000000000000000000000000000002i−2i2i−2i00
χ664-44-400000044-4-4-44000000000000000004-40000000000000000000000000000000000000000−2i2i−2i2i00
χ674-44-40000004-44-4-4400000000000000000-4400000000000000000000000000000000000000002i−2i−2i2i00
χ684-44-40000004-44-4-4400000000000000000-440000000000000000000000000000000000000000−2i2i2i−2i00
χ694-4-4444-4-44-4-200-222004i−4i0004i−4i00-22-222-2000000−2i2i0000−2i2i0000000000000000000000000000000000
χ704-4-4444-4-44-4-200-22200−4i4i000−4i4i00-22-222-20000002i−2i00002i−2i0000000000000000000000000000000000
χ714-4-444-444-4-4-200-222004i−4i000−4i4i00-222-2-22000000−2i2i00002i−2i0000000000000000000000000000000000
χ724-4-444-444-4-4-200-22200−4i4i0004i−4i00-222-2-220000002i−2i0000−2i2i0000000000000000000000000000000000
χ734-4-44-444-4-44-200-2224-400000004-42-2-2-2220000-2200-2200000000000000000000000000000000000000
χ744-4-44-444-4-44-200-222-440000000-442-2-2-22200002-2002-200000000000000000000000000000000000000
χ754-4-44-4-4-4444-200-2224-40000000-442-222-2-20000-22002-200000000000000000000000000000000000000
χ764-4-44-4-4-4444-200-222-4400000004-42-222-2-200002-200-2200000000000000000000000000000000000000
χ7788-8-8000000800-88-800000000000000000000000000000000000000000000000000000000000000000
χ7888-8-8000000-4004-44000000000000000000043−4300000000000000000000000000000000000000000000
χ7988-8-8000000-4004-440000000000000000000−434300000000000000000000000000000000000000000000
χ808-88-8000000-48-844-400000000000000000-440000000000000000000000000000000000000000000000
χ818-88-8000000-4-8844-4000000000000000004-40000000000000000000000000000000000000000000000

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