Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11395 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #393 |
| commutator | C24 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1446 |
| prime radical | C24×C11 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
820 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 250 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)(12,13,16,21,17,20,29,36)(14,18,24,32,23,31,28,37)(15,25,27,40,26,19,33,35)(22,34,39,43,38,30,41,42);(12,14)(13,18,20,31)(15,22)(16,28)(17,23)(19,34,25,30)(21,37,36,32)(24,29)(26,38)(27,41)(33,39)(35,42,40,43);(12,15)(13,19,20,25)(14,22)(16,27)(17,26)(18,30,31,34)(21,35,36,40)(23,38)(24,39)(28,41)(29,33)(32,42,37,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4383);