Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23×C4 |
| direct product | C23×#1961 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C2×D4 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C2×C23×#127 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G | |
412 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 128 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) = 1472 |
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)(25,27)(28,29,30,31)(32,33)(34,38)(35,39)(36,37);(29,31)(32,34,38,33,36,39,35,37);(24,25,26,27)(33,37)(34,39)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7116, C23×#7352, C23×#7504, … |
| maximal normal subgroup of | C23×#7116, C23×#7352, C23×#7504, … |
| maximal quotient of | C23×#9642, C23×#9648, C23×#9684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 693);