Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C23 · Schur multiplier (H2) = C25 |
| direct product | C23×#2913 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C22×D4 |
| commutator | C4 | C23×C4×C23 |
| Frattini, cosocle | C2×C4 | C24×C23 |
| prime radical | C2×#41×C23 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×#41×C23 ◁ G | |
476 conjugacy classes of subgroups; only the 344 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 344 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) = 1472 |
A minimal faithful permutation representation — 4 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)(29,33)(31,34)(35,39)(36,40)(38,41)(42,43);(28,29,34,40,32,36,31,33)(30,35,41,43,37,42,38,39);(28,30)(29,35)(31,38)(32,37)(33,39)(34,41)(36,42)(40,43);(30,37)(35,42)(38,41)(39,43)1012 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#12925, C23×#12926, C23×#12996, … |
| maximal normal subgroup of | C23×#12925, C23×#12926, C23×#12996, … |
| maximal quotient of | C23×#17789, C23×#17799, C23×#17812, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1645);