Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1685 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×#1697 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C19 |
| prime radical | C19×#459 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ G | |
170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(25,27)(28,29)(30,32)(31,33)(34,35);(20,21,22,24,23,25,26,27)(29,32)(33,34);(21,25)(24,27)(29,33)(31,35)(32,34)437 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C19×#1697, C19×#19142, C19×#19156, … |
| maximal normal subgroup of | C2×C19×#1697, C19×#19142, C19×#19156, … |
| maximal quotient of | C19×#8654, C19×#9223, C19×#9229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 429);