Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#1888 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #120 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C22×D4×C23 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G | |
344 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 112 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 — 3 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)(25,27)(28,29,34,37,33,30,32,36)(31,35,41,43,40,38,39,42);(24,25,26,27)(28,30,33,29)(31,38,40,35)(32,36,34,37)(39,42,41,43);(28,31,33,40)(29,35,30,38)(32,41,34,39)(36,43,37,42)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7481, C23×#7489, C23×#12774, … |
| maximal normal subgroup of | C23×#7481, C23×#7489, C23×#12774, … |
| maximal quotient of | C23×#8960, C23×#8964, C23×#9002, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 620);