Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C25 |
| direct product | C23×#2760 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C23 |
| prime radical | C23×#392 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
520 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 520 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) = 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)(25,28)(26,30)(32,33,36,34)(35,38,39,37)(40,41)(42,46)(43,44)(45,47);(25,28)(29,31)(33,34)(35,39)(41,44)(42,47);(24,25,27,28)(26,29,30,31)(32,34,36,33)(35,38,39,37)(40,42)(41,45)(43,47)(44,46);(24,26)(25,29)(27,30)(28,31)(32,35)(33,37)(34,38)(36,39)(40,41)(42,45)(43,44)(46,47)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#12187, C23×#12263, C23×#36776, … |
| maximal normal subgroup of | C23×#12187, C23×#12263, C23×#36776, … |
| maximal quotient of | C23×#14375, C23×#14508, C23×#14572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1492);