Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32947 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#32947 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3027 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1306 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)(16,27)(19,28)(20,29)(21,30)(22,34)(23,36)(25,37)(31,41)(32,39)(33,40)(38,42);(12,13,16,18,17,21,27,30)(14,19,23,28,24,32,36,39)(15,20,25,29,26,33,37,40)(22,31,35,38,34,42,43,41);(12,14)(13,19)(15,22)(16,23)(17,24)(18,28)(20,31)(21,32)(25,35)(26,34)(27,36)(29,38)(30,39)(33,42)(37,43)(40,41);(12,15)(13,20)(14,22)(16,25)(17,26)(18,29)(19,31)(21,33)(23,35)(24,34)(27,37)(28,38)(30,40)(32,42)(36,43)(39,41)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25935);