Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C27 |
| direct product | C23×#2847 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
1224 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 288 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 4 generators on 35 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)(29,31)(33,35);(32,33,34,35);(28,29)(30,31);(24,25)(26,27)(28,29)(30,31)1012 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#9113, C23×#9117, C23×#9147, … |
| maximal normal subgroup of | C23×#9113, C23×#9117, C23×#9147, … |
| maximal quotient of | C23×#14680, C23×#14694, C23×#14696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1579);