Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13343 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13419 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×D4 | C23×C11 |
| prime radical | C11×#2679 | C2 |
| LCS | G ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C11 ◁ C22×D4×C11 ◁ G | |
776 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 776 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) = 23 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,14)(17,20)(21,23);(12,13)(14,15)(18,22);(12,14,15,13)(16,17)(18,20)(19,21)(22,23)341 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6407);