Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#2049 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #394 |
| commutator, Frattini, cosocle | C22×C4 | C23×C19 |
| prime radical | C2×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
254 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 80 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)(20,21,26,31)(22,32,35,47)(23,36,40,45)(24,30,25,29)(27,41,43,34)(28,38,46,39)(33,44,37,42)(48,51,50,49);(20,22)(21,27)(23,37)(24,41)(25,34)(26,35)(28,44)(29,47)(30,32)(31,43)(33,40)(36,50)(38,49)(39,51)(42,46)(45,48);(20,23,24,38,26,40,25,39)(21,28,29,45,31,46,30,36)(22,33,34,49,35,37,41,51)(27,42,32,48,43,44,47,50)437 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C19×#2049, C19×#23525, C19×#24295, … |
| maximal normal subgroup of | C2×C19×#2049, C19×#23525, C19×#24295, … |
| maximal quotient of | C19×#10444, C19×#10445, C19×#10446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 781);