Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #13561 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#13566 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×AΣL(1,𝔽16) |
| commutator | C2×D4 | C22×C4×C11 |
| Frattini, cosocle | #124 | C23×C11 |
| prime radical | C11×#3018 | C2 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C22×C4×C11 ◁ C11×#532 ◁ G | |
478 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,22,18,23,31,37)(14,24,27,35,29,41,43,19)(15,20,30,21,17,32,33,38)(25,39,42,36,28,40,26,34);(12,14)(13,19)(15,28)(16,26)(17,25)(18,29)(20,36)(21,24)(22,39)(23,35)(27,33)(30,43)(31,42)(32,34)(37,40)(38,41);(12,15,18,17)(13,20,23,32)(14,25,29,28)(16,30,31,33)(19,34,35,36)(21,37,38,22)(24,39,41,40)(26,27,42,43)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6554);