Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×#1676 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C23 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C23 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ G | |
144 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 144 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) = 55 |
| transitive degree | μt(G) = 2944 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,31)(26,32,35,39)(27,36,33,30)(29,37,38,34)(40,41,44,47)(42,48,50,55)(43,51,53,46)(45,52,54,49);(24,26,33,37,28,35,27,34)(25,29,36,39,31,38,30,32);(40,42,44,50)(41,45,47,54)(43,52,53,49)(46,55,51,48)667 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#12384, C23×#12385, C23×#12386, … |
| maximal normal subgroup of | C23×#12384, C23×#12385, C23×#12386, … |
| maximal quotient of | C23×#8645, C23×#9216, C23×#9568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 408);