Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18192 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18200 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3490 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1078 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21)(14,22,25,38)(15,26,28,40)(16,19,30,34)(18,31,32,24)(20,35,37,29)(23,36,39,43)(27,33,41,42);(12,14)(13,18)(15,27)(16,23)(17,25)(19,33)(20,36)(21,32)(22,26)(24,29)(28,41)(30,39)(31,35)(34,42)(37,43)(38,40);(15,28)(20,37)(22,38)(24,31)(26,40)(27,41)(29,35)(36,43);(13,19)(14,23)(20,26)(21,34)(24,27)(25,39)(31,41)(37,40)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11188);