Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2221 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#2223 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #466 |
| commutator, Frattini, cosocle | C2×C8 | C23×C19 |
| prime radical | C19×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C19×#131 ◁ G | |
144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,27)(22,33)(23,36)(24,25)(28,37)(29,44)(30,41)(31,40)(32,42)(34,49)(35,38)(39,45)(46,51)(47,50);(20,21,28,40,25,31,23,27,26,32,36,41,24,30,37,42)(22,29,43,51,33,45,34,39,35,46,48,44,38,47,49,50);(20,22)(21,29)(23,34)(24,38)(25,33)(26,35)(27,39)(28,43)(30,47)(31,45)(32,46)(36,48)(37,49)(40,51)(41,44)(42,50)494 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C19×#2223, C19×#33617, C19×#33618, … |
| maximal normal subgroup of | C2×C19×#2223, C19×#33617, C19×#33618, … |
| maximal quotient of | C19×#12432, C19×#12435, C19×#12441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 955);