Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2021 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11391 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C24 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #379 |
| prime radical | C24×C11 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
842 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 254 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(20,21,24,29,25,28,37,42)(22,30,33,43,32,26,36,39)(23,27,35,40,34,41,47,51)(31,38,46,49,45,44,48,50);(12,13,15,17)(14,18,19,16)(20,22)(21,26)(23,31)(24,36)(25,32)(27,38)(28,30)(29,43)(33,37)(34,45)(35,48)(39,42)(40,50)(41,44)(46,47)(49,51);(12,14,15,19)(13,16,17,18)(20,23)(21,27)(22,31)(24,35)(25,34)(26,38)(28,41)(29,40)(30,44)(32,45)(33,46)(36,48)(37,47)(39,49)(42,51)(43,50)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4379);