Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×AGL(1,ℤ/16) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #442 |
| commutator | C8 | C22×C4×C23 |
| Frattini, cosocle | C2×C8 | C23×C23 |
| prime radical | C23×#509 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C23×#97 ◁ G | |
154 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 72 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)(25,29,31,38)(26,33)(27,34)(30,36,39,32)(35,37);(24,25)(26,30)(27,36)(28,31)(29,37)(32,34)(33,38)(35,39);(24,26,34,37,28,35,27,33)(25,30,32,29,31,39,36,38)529 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×AGL(1,ℤ/16), C23×#33468, C23×#33469, … |
| maximal normal subgroup of | C2×C23×AGL(1,ℤ/16), C23×#33468, C23×#33469, … |
| maximal quotient of | C23×#12065, C23×#12067, C23×#12077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 913);