Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11234 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11234 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #391 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1441 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
640 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)(14,23)(15,27,30,42)(16,31)(17,21)(18,22)(19,25)(20,29,37,28)(24,33,40,36)(26,34)(32,35)(38,39,41,43);(12,14,16,25,18,26,17,32)(13,19,21,23,22,35,31,34)(15,24,28,39,30,40,29,43)(20,36,27,41,37,33,42,38);(12,15,16,28,18,30,17,29)(13,20,21,27,22,37,31,42)(14,24,25,39,26,40,32,43)(19,33,23,38,35,36,34,41)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4222);