Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33557 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33561 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C11 |
| prime radical | C11×#3018 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C11×#41 ◁ G | |
1096 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)(15,20)(16,21)(17,22)(18,23)(19,26)(25,36)(27,34)(28,33)(29,37)(30,38)(31,39)(32,40)(35,41)(42,43);(12,14,18,15)(13,19,23,33)(16,27,30,25)(17,26,31,28)(20,22,24,39)(21,35,38,32)(29,41,42,40)(34,43,36,37);(12,15,18,14)(13,20,23,24)(16,25,30,27)(17,26,31,28)(19,22,33,39)(21,36,38,34)(29,41,42,40)(32,43,35,37);(12,16,18,30)(13,21,23,38)(14,25,15,27)(17,29,31,42)(19,32,33,35)(20,34,24,36)(22,37,39,43)(26,40,28,41)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26549);