Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23996 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23997 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2404 |
| commutator, Frattini, cosocle | C24 | C24×C11 |
| prime radical | C11×#3026 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C24×C11 ◁ G | |
1210 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)(14,18)(15,19)(16,20)(17,21)(22,29)(23,30)(24,31)(25,37)(26,39)(27,33)(28,34)(32,40)(35,43)(36,42)(38,41);(12,14,17,24)(13,18,21,31)(15,25)(16,23,28,36)(19,29)(20,30,34,42)(22,27)(26,38)(32,41)(33,37)(35,40)(39,43);(12,15)(13,19)(14,22)(16,26)(17,27)(18,29)(20,32)(21,33)(23,35)(24,25)(28,40)(30,41)(31,37)(34,39)(36,38)(42,43);(12,16)(13,20)(14,23)(15,26)(17,28)(18,30)(19,32)(21,34)(22,35)(24,36)(25,38)(27,40)(29,41)(31,42)(33,39)(37,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16985);