Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33551 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33554 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C11 |
| prime radical | C11×#3025 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C11×#41 ◁ G | |
1112 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)(15,19)(16,20)(17,21)(18,24)(23,36)(25,37)(26,40)(27,33)(28,34)(29,35)(30,38)(31,39)(32,41)(42,43);(12,14,17,25)(13,18,21,31)(15,26,28,23)(16,24,29,39)(19,32,34,30)(20,22,35,37)(27,41,42,38)(33,40,43,36);(16,29)(24,39)(27,42)(38,41);(12,15,17,28)(13,19,21,34)(14,23,25,26)(16,27,29,42)(18,30,31,32)(20,33,35,43)(22,36,37,40)(24,38,39,41)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26542);