Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2132 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | #99 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C2×Q8 | C23×C23 |
| socle | C2×C23 | C2×#99 |
| prime radical | C23×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C2×C4×C23 ◁ C2×#41×C23 ◁ G | |
250 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 84 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)(24,25,28,33,29,34,26,31)(27,32,35,39,36,30,37,38);(25,30)(27,36)(31,38)(32,34)(33,39)(35,37);(24,26,29,28)(25,31,34,33)(27,35,36,37)(30,38,32,39)598 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7484, C23×#7488, C23×#7492, … |
| maximal normal subgroup of | C23×#7484, C23×#7488, C23×#7492, … |
| maximal quotient of | C23×#11431, C23×#11447, C23×#11475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 864);