Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23990 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23993 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3021 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1152 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)(12,13,16,18)(14,19,24,31)(15,25,26,20)(17,29,28,21)(22,32,30,34)(23,33,37,38)(27,35,40,39)(36,42,41,43);(13,18)(14,22,24,30)(19,32,31,34)(20,25)(21,29)(23,36,37,41)(33,42,38,43)(35,39);(12,14)(13,19)(15,23)(16,24)(17,30)(18,31)(20,33)(21,32)(22,28)(25,38)(26,37)(27,41)(29,34)(35,42)(36,40)(39,43);(12,15)(13,20)(14,23)(16,26)(17,27)(18,25)(19,33)(21,35)(22,36)(24,37)(28,40)(29,39)(30,41)(31,38)(32,42)(34,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16981);