Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2863 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C23 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
408 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2944 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,29,28)(26,31,27,30)(32,33,36,39)(34,37,38,35)(42,46)(44,47);(24,26,29,27)(25,30,28,31)(32,34,36,38)(33,37,39,35)(40,41,43,45)(42,44,46,47);(24,27,29,26)(25,31,28,30)(32,35,36,37)(33,38,39,34);(24,28,29,25)(26,31,27,30)(32,33)(34,37)(35,38)(36,39)(40,42)(41,44)(43,46)(45,47)1012 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7669, C23×#7673, C23×#7689, … |
| maximal normal subgroup of | C23×#7669, C23×#7673, C23×#7689, … |
| maximal quotient of | C23×#14688, C23×#14699, C23×#14703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1595);