Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#1451 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C23 | C23 |
| commutator | C22 | C2×C42×C23 |
| Frattini, cosocle | C42 | C23×C23 |
| socle | C22×C23 | C2×C42 |
| prime radical | C23×C23 | C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C23 ◁ G | |
208 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,29,27,28,30,31)(33,36)(37,39);(32,33,34,37,35,36,38,39);(25,28)(29,31)1288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×#7164, C23×#7166, C23×#7210, … |
| maximal normal subgroup of | C23×#7164, C23×#7166, C23×#7210, … |
| maximal quotient of | C23×#7842, C23×#7848, C23×#8132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 183);