Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11363 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #397 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1445 |
| prime radical | C24×C11 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,23,18,21,16,22)(14,19,27,35,25,36,26,34)(15,28,30,38,32,39,31,20)(24,37,41,42,40,43,29,33);(12,14,16,27,18,25,17,26)(13,19,23,34,21,36,22,35)(15,29,30,40,32,41,31,24)(20,37,39,42,38,43,28,33);(12,15,16,30,18,32,17,31)(13,20,23,39,21,38,22,28)(14,24,27,29,25,40,26,41)(19,33,34,37,36,42,35,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4351);