Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23882 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23884 |
| 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 | |
1684 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)(14,24)(15,28)(16,22)(17,20)(18,23)(19,26)(21,29)(25,33)(27,35)(30,37)(31,36)(32,34)(38,39)(40,43)(41,42);(12,14)(13,19)(15,25)(16,32)(17,26)(18,27)(20,35)(21,33)(22,24)(23,34)(28,38)(29,41)(30,39)(31,40)(36,42)(37,43);(13,20)(16,17)(19,24)(21,36)(22,23)(26,32)(28,37)(29,30)(33,38)(34,35)(39,41)(42,43);(12,15,18,31)(13,21,23,37)(14,25,27,40)(16,30,17,29)(19,33,34,43)(20,36,22,28)(24,38,35,42)(26,41,32,39)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16872);