Finite Group Databasebeta

← Group #11778411

Character table — Group #11778411

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222244444444444444444488888888888888888888888824242424242424242424242424242424363648484848727272
order122222336666663446666666121212121212121266881212121224242424242424242424242424242424244444441212121212121212446121212288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111
χ51111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1
χ61111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-111
χ71111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-111
χ81111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-11-1-1
χ9222222222222222-2-22222222-2-2-2-2-2-2-2-22200-2-2-2-200000000000000000000000000000000220000-200
χ10222222222222222-2-22222222-2-2-2-2-2-2-2-22200-2-2-2-200000000000000000000000000000000-2-20000200
χ112222222-12-12-12-1-1222-1-1-1-1-1222-1-1-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1000000-1-100000
χ122222222-12-12-12-1-1222-1-1-1-1-1222-1-1-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011110000001100000
χ132222222-12-12-12-1-1222-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2-2-211111111111122-2-200001111000000-1-100000
χ142222222-12-12-12-1-1222-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2-2-2111111111111-2-2220000-1-1-1-10000001100000
χ15222222-12-12-12-12-122-122-1-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000022220000-1-1-1-10000-1-1000
χ16222222-12-12-12-12-122-122-1-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-200001111000011000
χ17222222-12-12-12-12-122-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-12-1-11111-2-2-2-211111111000022-2-2000011110000-1-1000
χ18222222-12-12-12-12-122-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-12-1-11111-2-2-2-2111111110000-2-2220000-1-1-1-1000011000
χ192222-2-22222222222-2-2-2-2222-222222222-2-200-2-2-2-200000000000000002-200000000000000002-200000
χ202222-2-22222222222-2-2-2-2222-222222222-2-200-2-2-2-20000000000000000-220000000000000000-2200000
χ212222-2-2222222222-22-2-2-2222-2-2-2-2-2-2-2-2-2-2-2002222000000000000000000002-200000000000000-22000
χ222222-2-2222222222-22-2-2-2222-2-2-2-2-2-2-2-2-2-2-200222200000000000000000000-22000000000000002-2000
χ232222-2-22-12-12-12-1-12-2-211-1-1-1-222-1-1-1-1-1-11100-21110000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i32-2000000−i3−i3i3i3000000-1100000
χ242222-2-22-12-12-12-1-12-2-211-1-1-1-222-1-1-1-1-1-11100-21110000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i3-22000000i3i3−i3−i30000001-100000
χ252222-2-22-12-12-12-1-12-2-211-1-1-1-222-1-1-1-1-1-11100-21110000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i32-2000000i3i3−i3−i3000000-1100000
χ262222-2-22-12-12-12-1-12-2-211-1-1-1-222-1-1-1-1-1-11100-21110000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i3-22000000−i3−i3i3i30000001-100000
χ272222-2-2-12-12-12-12-1-221-2-2-1-1-1111-2-211111100-12-1-133−3−3000033−3−333−3−300002-200000033−3−300001-1000
χ282222-2-2-12-12-12-12-1-221-2-2-1-1-1111-2-211111100-12-1-133−3−3000033−3−333−3−30000-22000000−3−3330000-11000
χ292222-2-2-12-12-12-12-1-221-2-2-1-1-1111-2-211111100-12-1-1−3−3330000−3−333−3−33300002-2000000−3−33300001-1000
χ302222-2-2-12-12-12-12-1-221-2-2-1-1-1111-2-211111100-12-1-1−3−3330000−3−333−3−3330000-2200000033−3−30000-11000
χ3122-2-2-22222-2-22-2-2200-22-22-2-22000000002-2−i2i20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000002i−2i000002−2
χ3222-2-2-22222-2-22-2-2200-22-22-2-22000000002-2−i2i20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000−2i2i00000−22
χ3322-2-2-22222-2-22-2-2200-22-22-2-22000000002-2i2−i20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000002i−2i00000−22
χ3422-2-2-22222-2-22-2-2200-22-22-2-22000000002-2i2−i20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000−2i2i000002−2
χ354444444-24-24-24-2-2-4-44-2-2-2-2-24-4-4222222-2-200-422200000000000000000000000000000000000000000
χ36444444-24-24-24-24-2-4-4-244-2-2-2-222-4-42222-2-2002-42200000000000000000000000000000000000000000
χ37444444-2-2-2-2-2-2-2-2144-2-2-2111-2-2-2-2-211111144-2-211-2-2-2-2-2-2-2-2111111110000000000000000000000000
χ38444444-2-2-2-2-2-2-2-2144-2-2-2111-2-2-2-2-2111111-4-4-2-21122222222-1-1-1-1-1-1-1-10000000000000000000000000
χ39444444-2-2-2-2-2-2-2-21-4-4-2-2-2111-22222-1-1-1-1110022-1-1000000003i3i−3i−3i−3i−3i3i3i0000000000000000000000000
χ40444444-2-2-2-2-2-2-2-21-4-4-2-2-2111-22222-1-1-1-1110022-1-100000000−3i−3i3i3i3i3i−3i−3i0000000000000000000000000
χ414444-4-44-24-24-24-2-2-44-422-2-2-2-4-4-422222222004-2-2-200000000000000000000000000000000000000000
χ424444-4-4-24-24-24-24-24-42-4-4-2-2-22-2-244-2-2-2-222002-42200000000000000000000000000000000000000000
χ434444-4-4-2-2-2-2-2-2-2-214-42221112-2-2-2-21111-1-10022-1-10000−2i3−2i32i32i3i3i3i3i3−i3−i3−i3−i30000000000000000000000000
χ444444-4-4-2-2-2-2-2-2-2-214-42221112-2-2-2-21111-1-10022-1-100002i32i3−2i3−2i3−i3−i3−i3−i3i3i3i3i30000000000000000000000000
χ454444-4-4-2-2-2-2-2-2-2-21-4422211122222-1-1-1-1-1-100-2-2112323−23−230000−3−333−3−3330000000000000000000000000
χ464444-4-4-2-2-2-2-2-2-2-21-4422211122222-1-1-1-1-1-100-2-211−23−232323000033−3−333−3−30000000000000000000000000
χ4744-4-44-4444-4-44-4-44004-444-4-4-400000000-4400000000000000000000000000000000000000000000000
χ4844-4-44-44-242-4-2-42-20042-2-222-4000000002-200000000006−6−666−66−6−66−660000000000000000000000000
χ4944-4-44-44-242-4-2-42-20042-2-222-4000000002-20000000000−666−6−66−666−66−60000000000000000000000000
χ5044-4-44-4-24-2-4242-4-200-2-44-2222000000002-2000000i6−i6−i6i60000i6−i6−i6i6i6−i6−i6i60000000000000000000000000
χ5144-4-44-4-24-2-4242-4-200-2-44-2222000000002-2000000−i6i6i6−i60000−i6i6i6−i6−i6i6i6−i60000000000000000000000000
χ5244-4-44-4-2-2-222-222100-22-21-1-1200003i3i−3i−3i-1100003i−3ii6−i6−i6i66−6−66−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000000
χ5344-4-44-4-2-2-222-222100-22-21-1-1200003i3i−3i−3i-1100003i−3i−i6i6i6−i6−666−6ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000000
χ5444-4-44-4-2-2-222-222100-22-21-1-120000−3i−3i3i3i-110000−3i3ii6−i6−i6i6−666−6−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000000
χ5544-4-44-4-2-2-222-222100-22-21-1-120000−3i−3i3i3i-110000−3i3i−i6i6i6−i66−6−66ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000000
χ5644-4-4-444-242-4-2-42-200-4-22-222400000000-22−2i22i20000−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000000000000
χ5744-4-4-444-242-4-2-42-200-4-22-222400000000-222i2−2i200002i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000
χ5844-4-4-44-24-2-4242-4-20024-4-222-200000000-22−2i22i20000i2−i2i2−i2−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i20000000000000000000000000
χ5944-4-4-44-24-2-4242-4-20024-4-222-200000000-222i2−2i20000−i2i2−i2i22i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000
χ6044-4-4-44-2-2-222-2221002-221-1-1-200003i3i−3i−3i1-1−2i22i200−3i3ii2−i2i2−i2i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ230000000000000000000000000
χ6144-4-4-44-2-2-222-2221002-221-1-1-200003i3i−3i−3i1-12i2−2i200−3i3i−i2i2−i2i2−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ230000000000000000000000000
χ6244-4-4-44-2-2-222-2221002-221-1-1-20000−3i−3i3i3i1-1−2i22i2003i−3ii2−i2i2−i2i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ230000000000000000000000000
χ6344-4-4-44-2-2-222-2221002-221-1-1-20000−3i−3i3i3i1-12i2−2i2003i−3i−i2i2−i2i2−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ230000000000000000000000000
χ644-44-40044-4-4-4-444400000-4-44000000000000000000000000000000000002-200002-22-20000000000000
χ654-44-40044-4-4-4-444400000-4-4400000000000000000000000000000000000-220000-22-220000000000000
χ664-44-4004-2-42-424-2-20000022-2000−2i32i3−2i32i3−2i32i3000000000000000000000000002-20000−1+i31−i3−1−i31+i30000000000000
χ674-44-4004-2-42-424-2-20000022-2000−2i32i3−2i32i3−2i32i300000000000000000000000000-2200001−i3−1+i31+i3−1−i30000000000000
χ684-44-4004-2-42-424-2-20000022-20002i3−2i32i3−2i32i3−2i3000000000000000000000000002-20000−1−i31+i3−1+i31−i30000000000000
χ694-44-4004-2-42-424-2-20000022-20002i3−2i32i3−2i32i3−2i300000000000000000000000000-2200001+i3−1−i31−i3−1+i30000000000000
χ704-4-440044-444-4-4-4400000-44-40000000000000000000000000000000000000002i−2i00002i−2i2i−2i000000000
χ714-4-440044-444-4-4-4400000-44-4000000000000000000000000000000000000000−2i2i0000−2i2i−2i2i000000000
χ724-4-4400-2424-2-42-4-2000002-22023−230023−23−23230000000000000000000000000000002i−2i0000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000
χ734-4-4400-2424-2-42-4-2000002-22023−230023−23−2323000000000000000000000000000000−2i2i0000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000
χ744-4-4400-2424-2-42-4-2000002-220−232300−232323−230000000000000000000000000000002i−2i0000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000
χ754-4-4400-2424-2-42-4-2000002-220−232300−232323−23000000000000000000000000000000−2i2i0000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000
χ768-88-800-484-84-8-48-40000044-40000000000000000000000000000000000000000000000000000000000
χ778-88-800-4-44444-4-4200000-2-22000−4i34i32i3−2i32i3−2i30000000000000000000000000000000000000000000000000
χ788-88-800-4-44444-4-4200000-2-220004i3−4i3−2i32i3−2i32i30000000000000000000000000000000000000000000000000
χ798-8-88008-4-8-484-84-4000004-440000000000000000000000000000000000000000000000000000000000
χ808-8-8800-4-44-4-4444200000-22-2043−4300−232323−230000000000000000000000000000000000000000000000000
χ818-8-8800-4-44-4-4444200000-22-20−43430023−23−23230000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.