Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23×C4 |
| direct product | C23×#1875 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C2×D4 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C2×C23×#121 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C23×C4×C23 ◁ G | |
412 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 128 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)(25,27)(28,29)(30,31)(32,33,37,38,36,34,35,39);(24,25,26,27)(32,34,36,33)(35,39,37,38);(29,31)(32,35,36,37)(33,38,34,39)874 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#8487, C2×C23×#1875, C23×#20908, … |
| maximal normal subgroup of | C23×#8487, C2×C23×#1875, C23×#20908, … |
| maximal quotient of | C23×#8940, C23×#8943, C23×#8978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 607);