Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4×C11 · Schur multiplier (H2) = C215 |
| direct product | C24×C11×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C26×C11 | C22 |
| commutator | C2 | C25×C4×C11 |
| Frattini, cosocle | C22 | C26×C11 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C26×C11 ◁ G | |
19742 conjugacy classes of subgroups; only the 15454 normal subgroups are shown.
This group has 19742 conjugacy classes of subgroups — too many to draw. Only its 15454 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 6 generators on 27 points:
(1,2)(17,18,19,20,21,22,23,24,25,26,27);(3,4);(5,6);(7,8);(10,12)(13,14,15,16);(9,10,11,12)1760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 55628);