Finite Group Databasebeta

← Group #13149581

Character table — Group #13149581

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666699991212121212121212181818181818181818181818181824242424242424242424363636363636363636363636363636363636363672727272
order1222344666441212121212123366666622223666121212124444444444666612121212121212121212444444121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111111111-11-1-11-1-1-1-1-1-1-111-1-111-1-11-11-1
χ411111111111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111111111-1-11-1-11-1-1-1-1-1-1-1-111-1-111-11-11
χ51111111111-1-1-1-111-1-11111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ61111111111-1-1-1-111-1-111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-111-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-1-1-111-1-111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1111-1-11111-1-111-1-1-11-11
χ81111111111-1-1-1-111-1-111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-111-111-1-111-1-111-1-1111-11-1
χ911111-1-11111-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ1011111-1-11111-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-111-1-1-1-111-1-1-1-11111-1-111
χ1111111-1-11111-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-1-1-111-11-11-111111-1-111-1-1-1-1111-1-11
χ1211111-1-11111-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1111-11111-1-1-1-11111-1-1-111-1
χ1311111-1-1111-1111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111
χ1411111-1-1111-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1111111-1-1
χ1511111-1-1111-1111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-11-11-1-1-1111111-1-1-1-111-111-1
χ1611111-1-1111-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11-1-11111-1-11111-1-11-1-11
χ172222222222222222222-12-12-12-10000-1-1-1-122-1-1002200002200002-12-1-1-1-1-1-1-100200200000000-1-100-1-10-10-1
χ182222222222222222222-12-12-12-10000-1-1-1-122-1-100-2-20000-2-200002-12-1-1-1-1-1-1-100-200-2000000001100110101
χ19222222222222222222-12-12-12-120000-1-1-1-1-1-12222000022000000-12-12-1-1-1-1-1-1020020000000-1-100-1-100-10-10
χ20222222222222222222-12-12-12-120000-1-1-1-1-1-122-2-20000-2-2000000-12-12-1-1-1-1-1-10-200-20000000110011001010
χ212222222222-2-2-2-222-2-22-12-12-12-10000-1-1-1-122-1-100220000220000-21-2111-1-11100-200-200000000-1-100-1-10101
χ222222222222-2-2-2-222-2-22-12-12-12-10000-1-1-1-122-1-100-2-20000-2-20000-21-2111-1-111002002000000001100110-10-1
χ232222222222-2-2-2-222-2-2-12-12-12-120000-1-1-1-1-1-122220000220000001-21-211-1-1110-200-20000000-1-100-1-1001010
χ242222222222-2-2-2-222-2-2-12-12-12-120000-1-1-1-1-1-122-2-20000-2-20000001-21-211-1-11102002000000011001100-10-10
χ2522222-2-22222-2-2-2-2-2222-12-12-12-10000-1-1-1-1-2-21100220000-2-200002-1-211111-1-100200-200000000-1-100110-101
χ2622222-2-22222-2-2-2-2-2222-12-12-12-10000-1-1-1-1-2-21100-2-200002200002-1-211111-1-100-2002000000001100-1-1010-1
χ2722222-2-22222-2-2-2-2-222-12-12-12-120000-1-1-1-111-2-2220000-2-2000000-121-21111-1-10200-20000000-1-1001100-1010
χ2822222-2-22222-2-2-2-2-222-12-12-12-120000-1-1-1-111-2-2-2-2000022000000-121-21111-1-10-200200000001100-1-10010-10
χ2922222-2-2222-2222-2-2-2-22-12-12-12-10000-1-1-1-1-2-21100220000-2-20000-212-1-1-1111100-200200000000-1-10011010-1
χ3022222-2-2222-2222-2-2-2-22-12-12-12-10000-1-1-1-1-2-21100-2-20000220000-212-1-1-1111100200-2000000001100-1-10-101
χ3122222-2-2222-2222-2-2-2-2-12-12-12-120000-1-1-1-111-2-2220000-2-20000001-2-12-1-111110-20020000000-1-100110010-10
χ3222222-2-2222-2222-2-2-2-2-12-12-12-120000-1-1-1-111-2-2-2-20000220000001-2-12-1-111110200-200000001100-1-100-1010
χ3322-2-22002-2-2000000002222-2-2-2-222-2-222-2-200002-22-200000022-2-200000000000000000000002-22-200000000
χ3422-2-22002-2-2000000002222-2-2-2-222-2-222-2-20000-22-2200000022-2-20000000000000000000000-22-2200000000
χ3522-2-22002-2-2000000002222-2-2-2-2-2-22222-2-200002-2-22000000-2-22200000000000000000000002-2-2200000000
χ3622-2-22002-2-2000000002222-2-2-2-2-2-22222-2-20000-222-2000000-2-2220000000000000000000000-222-200000000
χ372-22-2200-2-220000000022-2-222-2-22-22-22-2-2200000000002i−2i2i−2i2-22-2000000000000000000000000002i−2i2i−2i0000
χ382-22-2200-2-220000000022-2-222-2-22-22-22-2-220000000000−2i2i−2i2i2-22-200000000000000000000000000−2i2i−2i2i0000
χ392-22-2200-2-220000000022-2-222-2-2-22-222-2-2200000000002i−2i−2i2i-22-22000000000000000000000000002i−2i−2i2i0000
χ402-22-2200-2-220000000022-2-222-2-2-22-222-2-220000000000−2i2i2i−2i-22-2200000000000000000000000000−2i2i2i−2i0000
χ412-2-2222i−2i-22-200002i−2i0022-2-2-2-2222-2-222-22-22i−2i2i−2i00002i−2i00002-2-220000002i−2i00000000002i−2i00000000000000
χ422-2-2222i−2i-22-200002i−2i0022-2-2-2-222-222-22-22-22i−2i2i−2i0000−2i2i0000-222-20000002i−2i0000000000−2i2i00000000000000
χ432-2-222−2i2i-22-20000−2i2i0022-2-2-2-2222-2-222-22-2−2i2i−2i2i0000−2i2i00002-2-22000000−2i2i0000000000−2i2i00000000000000
χ442-2-222−2i2i-22-20000−2i2i0022-2-2-2-222-222-22-22-2−2i2i−2i2i00002i−2i0000-222-2000000−2i2i00000000002i−2i00000000000000
χ45444444444444444444-2-2-2-2-2-2-2-200001111-2-2-2-200000000000000-2-2-2-2111111000000000000000000000000
χ464444444444-4-4-4-444-4-4-2-2-2-2-2-2-2-200001111-2-2-2-2000000000000002222-1-111-1-1000000000000000000000000
χ4744444-4-44444-4-4-4-4-444-2-2-2-2-2-2-2-200001111222200000000000000-2-222-1-1-1-111000000000000000000000000
χ4844444-4-4444-4444-4-4-4-4-2-2-2-2-2-2-2-20000111122220000000000000022-2-211-1-1-1-1000000000000000000000000
χ4944-4-44004-4-4000000004-24-2-42-420000-2-2220000004-40000000000000000000000000000000000-2200000000
χ5044-4-44004-4-4000000004-24-2-42-420000-2-222000000-4400000000000000000000000000000000002-200000000
χ5144-4-44004-4-400000000-24-242-42-40000-2-22200004-40000000000000000000000000000000000-220000000000
χ5244-4-44004-4-400000000-24-242-42-40000-2-2220000-4400000000000000000000000000000000002-20000000000
χ534-44-4400-4-44000000004-2-424-2-420000-222-20000000000004i−4i00000000000000000000000000000000−2i2i0000
χ544-44-4400-4-44000000004-2-424-2-420000-222-2000000000000−4i4i000000000000000000000000000000002i−2i0000
χ554-44-4400-4-4400000000-242-4-242-40000-222-200000000004i−4i00000000000000000000000000000000−2i2i000000
χ564-44-4400-4-4400000000-242-4-242-40000-222-20000000000−4i4i000000000000000000000000000000002i−2i000000
χ574-4-4444i−4i-44-400004i−4i004-2-42-424-20000-22-224i−4i−2i2i00000000000000000000−2i2i00000000000000000000000000
χ584-4-4444i−4i-44-400004i−4i00-242-42-4-240000-22-22−2i2i4i−4i00000000000000000000−2i2i00000000000000000000000000
χ594-4-4444i−4i-44-400004i−4i00-2-22222-2-200001-11-1−2i2i−2i2i0000000000000000003-3i−i3i−3i000000000000000000000000
χ604-4-4444i−4i-44-400004i−4i00-2-22222-2-200001-11-1−2i2i−2i2i000000000000000000-33i−i−3i3i000000000000000000000000
χ614-4-444−4i4i-44-40000−4i4i004-2-42-424-20000-22-22−4i4i2i−2i000000000000000000002i−2i00000000000000000000000000
χ624-4-444−4i4i-44-40000−4i4i00-242-42-4-240000-22-222i−2i−4i4i000000000000000000002i−2i00000000000000000000000000
χ634-4-444−4i4i-44-40000−4i4i00-2-22222-2-200001-11-12i−2i2i−2i0000000000000000003-3−ii−3i3i000000000000000000000000
χ644-4-444−4i4i-44-40000−4i4i00-2-22222-2-200001-11-12i−2i2i−2i000000000000000000-33−ii3i−3i000000000000000000000000
χ656666-366-3-3-366-3-3-3-3-3-3000000002222000000000000220000-1-1-1-10000000000200200-1-1-1-1-1-1000000000000
χ666666-366-3-3-366-3-3-3-3-3-300000000-2-2-2-2000000000000-2-2000011110000000000-200-200111111000000000000
χ676666-366-3-3-3-6-633-3-333000000002222000000000000220000-1-1-1-10000000000-200-20011-1-111000000000000
χ686666-366-3-3-3-6-633-3-33300000000-2-2-2-2000000000000-2-2000011110000000000200200-1-111-1-1000000000000
χ696666-3-6-6-3-3-36-63333-3-3000000002222000000000000-2-20000-1-1-1-10000000000200-2001111-1-1000000000000
χ706666-3-6-6-3-3-36-63333-3-300000000-2-2-2-200000000000022000011110000000000-200200-1-1-1-111000000000000
χ716666-3-6-6-3-3-3-66-3-33333000000002222000000000000-2-20000-1-1-1-10000000000-200200-1-11111000000000000
χ726666-3-6-6-3-3-3-66-3-3333300000000-2-2-2-200000000000022000011110000000000200-20011-1-1-1-1000000000000
χ736-6-66-36i−6i3-3300−3i33i3−3i3i33−33000000002-2-220000000000002i−2i0000-111-10000000000000000−i3i3−ii3−3000000000000
χ746-6-66-36i−6i3-3300−3i33i3−3i3i33−3300000000-222-2000000000000−2i2i00001-1-110000000000000000i3−i3i−i−33000000000000
χ756-6-66-36i−6i3-33003i3−3i3−3i3i−3333000000002-2-220000000000002i−2i0000-111-10000000000000000i3−i3−ii−33000000000000
χ766-6-66-36i−6i3-33003i3−3i3−3i3i−333300000000-222-2000000000000−2i2i00001-1-110000000000000000−i3i3i−i3−3000000000000
χ776-6-66-3−6i6i3-3300−3i33i33i−3i−3333000000002-2-22000000000000−2i2i0000-111-10000000000000000−i3i3i−i−33000000000000
χ786-6-66-3−6i6i3-3300−3i33i33i−3i−333300000000-222-20000000000002i−2i00001-1-110000000000000000i3−i3−ii3−3000000000000
χ796-6-66-3−6i6i3-33003i3−3i33i−3i33−33000000002-2-22000000000000−2i2i0000-111-10000000000000000i3−i3i−i3−3000000000000
χ806-6-66-3−6i6i3-33003i3−3i33i−3i33−3300000000-222-20000000000002i−2i00001-1-110000000000000000−i3i3−ii−33000000000000
χ8188-8-88008-8-800000000-4-4-4-44444000022-2-20000000000000000000000000000000000000000000000000000
χ828-88-8800-8-8800000000-4-444-4-44400002-2-220000000000000000000000000000000000000000000000000000
χ831212-12-12-600-666000000000000000044-4-4000000000000000000-2-2220000000000000000000000000000000000
χ841212-12-12-600-6660000000000000000-4-44400000000000000000022-2-20000000000000000000000000000000000
χ8512-1212-12-60066-600000000000000004-44-4000000000000000000-22-220000000000000000000000000000000000
χ8612-1212-12-60066-60000000000000000-44-440000000000000000002-22-20000000000000000000000000000000000

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