Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1913 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#1914 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #386 |
| commutator | C23 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C23×#535 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C4×C23 ◁ G | |
340 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 108 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)(24,25,28,32,29,31,38,26)(27,34,36,39,35,30,37,33);(24,26,28,31,29,32,38,25)(27,33,37,34,35,39,36,30);(24,27)(25,30)(26,33)(28,37)(29,35)(31,34)(32,39)(36,38)667 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#12755, C23×#12756, C23×#12769, … |
| maximal normal subgroup of | C23×#12755, C23×#12756, C23×#12769, … |
| maximal quotient of | C23×#9107, C23×#9109, C23×#9187, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 646);