Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2120 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | #99 |
| commutator | C23 | C22×C4×C23 |
| Frattini, cosocle | C2×D4 | C23×C23 |
| socle | C2×C23 | C2×#99 |
| prime radical | C23×#525 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C2×C4×C23 ◁ C2×#41×C23 ◁ G | |
264 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 368 |
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)(26,30)(27,34,35,29)(28,31)(32,38,39,36)(33,37);(25,29)(30,36)(31,34)(37,38);(24,26,28,33)(25,30,31,37)(27,32,35,39)(29,36,34,38)598 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#12623, C23×#12624, C23×#12711, … |
| maximal normal subgroup of | C23×#12623, C23×#12624, C23×#12711, … |
| maximal quotient of | C23×#11425, C23×#11452, C23×#11471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 852);