Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C2×C42 |
| direct product | C23×#2736 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C23 |
| prime radical | C25×C23 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
560 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 176 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) = 736 |
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)(27,28)(29,31)(32,33,36,37)(34,38,39,35)(40,41,43,45)(42,46,47,44);(25,28)(26,31)(33,37)(35,38)(40,41,43,45)(42,44,47,46);(24,26)(25,29)(27,31)(28,30)(32,34)(33,35)(36,39)(37,38)(40,41)(42,44)(43,45)(46,47);(24,25)(26,29)(27,28)(30,31)(32,35)(33,34)(36,38)(37,39)(40,42)(41,44)(43,47)(45,46)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#12188, C23×#12264, C23×#36725, … |
| maximal normal subgroup of | C23×#12188, C23×#12264, C23×#36725, … |
| maximal quotient of | C23×#14366, C23×#14481, C23×#14577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1468);