Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C26 |
| direct product | C23×#2614 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C23 |
| prime radical | C22×D4×C23 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
782 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 232 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)(29,31)(32,33,36,39)(34,40,42,37)(35,38,44,43)(41,46,47,45);(25,27)(29,31)(32,34,36,42)(33,37,39,40)(35,41,44,47)(38,45,43,46);(24,25)(26,27)(28,29)(30,31)(32,33)(34,40)(35,43)(36,39)(37,42)(38,44)(41,45)(46,47);(32,35)(33,38)(34,41)(36,44)(37,45)(39,43)(40,46)(42,47)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#18225, C23×#18227, C23×#23905, … |
| maximal normal subgroup of | C23×#18225, C23×#18227, C23×#23905, … |
| maximal quotient of | C23×#14256, C23×#14263, C23×#14301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1346);