Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32950 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#32951 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1298 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)(13,18)(14,23)(16,19)(21,31)(22,32)(24,39)(25,26)(27,28)(30,34)(33,42)(36,37)(38,40);(12,13,19,32,17,22,16,18)(14,20,23,34,26,35,25,30)(15,21,28,36,29,37,27,31)(24,33,38,43,40,42,39,41);(12,14)(13,20)(15,24)(16,25)(17,26)(18,30)(19,23)(21,33)(22,35)(27,39)(28,38)(29,40)(31,41)(32,34)(36,43)(37,42);(12,15)(13,21)(14,24)(16,27)(17,29)(18,31)(19,28)(20,33)(22,37)(23,38)(25,39)(26,40)(30,41)(32,36)(34,43)(35,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25939);