Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#2816 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| prime radical | C2×C19×#121 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
528 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(25,28)(29,31)(32,33,36,39)(34,35,38,37);(21,23)(25,28)(26,30)(32,34,36,38)(33,37,39,35);(20,21)(22,23)(24,25)(26,29)(27,28)(30,31)(32,34)(33,37)(35,39)(36,38);(24,26)(25,29)(27,30)(28,31)(32,35,36,37)(33,38,39,34)494 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#9981, C19×#9984, C19×#18451, … |
| maximal normal subgroup of | C19×#9981, C19×#9984, C19×#18451, … |
| maximal quotient of | C19×#14622, C19×#14624, C19×#14625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1548);