Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#11402 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C8×C11 | C23 |
| commutator | C22 | C2×C4×C8×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C2×C4×C8 |
| prime radical | C23×C11 | C4×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C4×C8×C11 ◁ G | |
322 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 246 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,17,15,16,18,19);(13,16)(17,19)(20,21,22,26,23,27,28,33,24,25,29,31,30,32,34,35);(21,25)(26,31)(27,32)(33,35)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4390);