Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33690 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#2190 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C11×M16 ◁ G | |
526 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)(14,19)(15,25)(16,29)(17,33)(18,22)(20,28)(21,30)(23,40)(24,39)(26,38)(27,42)(31,34)(32,37)(35,41)(36,43);(12,14,18,17)(13,19,22,33)(15,23,27,26)(16,30,32,24)(20,34,35,36)(21,37,39,29)(25,38,42,40)(28,43,41,31);(12,15)(13,20)(14,23)(16,31)(17,26)(18,27)(19,34)(21,38)(22,35)(24,41)(25,29)(28,30)(32,43)(33,36)(37,42)(39,40);(15,26,27,23)(16,32)(20,34,35,36)(21,39)(24,30)(25,38,42,40)(28,31,41,43)(29,37)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26678);