Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#2980 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C24 |
| commutator | C22 | C23×C4×C23 |
| Frattini, cosocle | C2×C4 | C24×C23 |
| socle | C22×C23 | C23×C4 |
| prime radical | C23×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ G | |
394 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 248 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) = 1472 |
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)(26,30)(27,29)(28,31)(32,33,35,39,36,40,43,47)(34,37,42,44,41,38,45,46);(24,26)(25,28)(27,31)(29,30)(32,34)(33,37)(35,42)(36,41)(38,40)(39,44)(43,45)(46,47);(26,31)(28,30)(32,34)(33,38)(35,42)(36,41)(37,40)(39,46)(43,45)(44,47);(25,29)(28,30)(34,41)(37,38)(42,45)(44,46)874 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#8918, C23×#9005, C23×#9007, … |
| maximal normal subgroup of | C23×#8918, C23×#9005, C23×#9007, … |
| maximal quotient of | C23×#20532, C23×#20539, C23×#20563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1712);