Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23897 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23898 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1718 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)(15,25)(16,28)(17,21)(19,27)(20,30)(22,37)(23,40)(24,33)(26,36)(29,35)(31,39)(32,42)(34,41)(38,43);(12,14,17,24)(13,18,21,33)(15,22,26,38)(16,23,30,42)(19,34,35,31)(20,32,28,40)(25,43,36,37)(27,39,29,41);(12,15)(13,19)(14,22)(16,29)(17,26)(18,31)(20,36)(21,35)(23,41)(24,38)(25,28)(27,30)(32,43)(33,34)(37,40)(39,42);(16,30)(20,28)(23,42)(25,36)(27,29)(32,40)(37,43)(39,41)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16886);