Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2238 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×#2238 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #481 |
| commutator, Frattini, cosocle | C2×C8 | C23×C23 |
| prime radical | C23×#469 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C2×M16×C23 ◁ G | |
134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 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)(26,32)(27,35)(30,37)(31,34)(33,39)(36,38);(26,33)(29,37)(32,39)(34,38);(24,25,27,36,28,30,35,31)(26,34,32,37,33,38,39,29)460 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#12298, C23×#12300, C23×#12301, … |
| maximal normal subgroup of | C23×#12298, C23×#12300, C23×#12301, … |
| maximal quotient of | C23×#12875, C23×#12931, C23×#13010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 970);