Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C23×C11×SD32 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C11 | D8 |
| commutator, Frattini, cosocle | C8 | C25×C11 |
| prime radical | C23×C11×D8 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
2334 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.
This group has 2334 conjugacy classes of subgroups — too many to draw. Only its 1054 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33);(3,4);(5,6);(7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22);(8,14)(9,21)(10,12)(11,19)(13,17)(16,22)(18,20)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 55614);