Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24409 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1336 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)(14,22,25,18)(15,26)(16,20)(17,21)(19,28)(23,40,41,33)(24,38,31,34)(27,43,42,35)(29,39)(30,37)(32,36);(12,14)(13,18)(15,27)(16,25)(17,31)(19,35)(20,22)(21,38)(23,29)(24,30)(26,43)(28,42)(32,41)(33,36)(34,37)(39,40);(12,15)(13,19)(14,23)(16,28)(17,32)(18,33)(20,26)(21,39)(22,40)(24,42)(25,41)(27,31)(29,30)(34,43)(35,38)(36,37);(12,14)(13,18)(15,23)(16,25)(17,24)(19,33)(20,22)(21,34)(26,40)(27,29)(28,41)(30,31)(32,42)(35,36)(37,38)(39,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17397);