Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1909 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#1912 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #386 |
| commutator | C2×C4 | C22×C4×C19 |
| Frattini, cosocle | C22×C4 | C23×C19 |
| prime radical | C2×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
314 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 108 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)(20,21,25,29,26,30,24,40)(22,31,35,42,34,46,33,27)(23,36,38,44,39,28,37,43)(32,45,49,41,48,51,47,50);(20,22)(21,27,30,42)(23,32)(24,33)(25,35)(26,34)(28,41,36,50)(29,31,40,46)(37,47)(38,49)(39,48)(43,51,44,45);(20,23,26,39)(21,28,30,36)(22,32,34,48)(24,38,25,37)(27,41,42,50)(29,44,40,43)(31,45,46,51)(33,49,35,47)551 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12781, C19×#12782, C2×C19×#1912, … |
| maximal normal subgroup of | C19×#12781, C19×#12782, C2×C19×#1912, … |
| maximal quotient of | C19×#9100, C19×#9102, C19×#9104, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 644);