Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#1386 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #102 |
| commutator | C8 | C42×C23 |
| Frattini, cosocle | C22×C8 | C22×C23 |
| prime radical | C23×C23 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C22×C8×C23 ◁ G | |
140 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 2 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27)(28,29,32,36)(30,31,38,40)(33,35,41,43)(34,42,39,37);(28,30,33,37,34,35,40,36,32,38,41,42,39,43,31,29)736 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#1386, C23×#12567, C4×C23×#360, … |
| maximal normal subgroup of | C2×C23×#1386, C23×#12567, C4×C23×#360, … |
| maximal quotient of | C23×#7158, C23×#7175, C23×#7178, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 118);