Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12711 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#12714 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1781 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C2×#41 | C23×C11 |
| prime radical | C11×#3487 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C11×2−1+4 ◁ G | |
974 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)(14,24)(15,27,29,38)(16,30,32,21)(17,22)(18,23)(19,26,35,31)(20,25,37,33)(28,41)(34,42)(36,39)(40,43);(12,14,18,17)(13,19,23,35)(15,25,29,33)(16,26,32,31)(20,34,37,41)(21,24,30,22)(27,40,38,36)(28,39,42,43);(12,15,18,29)(13,20,23,37)(14,25,17,33)(16,28,32,42)(19,34,35,41)(21,36,30,40)(22,38,24,27)(26,39,31,43)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 5702);