Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2199 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13052 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C11 |
| Frattini, cosocle | C2×#41 | C23×C11 |
| socle | C2×C11 | #1889 |
| prime radical | C11×#3018 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C2×C4×C11 ◁ C2×C11×#41 ◁ G | |
624 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 114 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)(12,13,17,22,15,20,24,33)(14,23,27,39,25,18,32,35)(16,21,30,38,28,19,31,37)(26,36,40,43,29,34,41,42);(12,14,24,32,15,25,17,27)(13,18,33,39,20,23,22,35)(16,29,30,41,28,26,31,40)(19,36,37,43,21,34,38,42);(13,19)(14,25)(16,28)(18,34)(20,21)(22,38)(23,36)(27,32)(30,31)(33,37)(35,43)(39,42)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6040);