Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1795 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#1795 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #379 |
| commutator | C2×C4 | C22×C4×C19 |
| Frattini, cosocle | C22×C4 | C23×C19 |
| prime radical | C2×C19×H(5,𝔽2) | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
588 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 132 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) = 304 |
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)(20,21)(22,29,31,26)(23,25)(24,28)(27,32)(30,34,35,33);(21,25)(23,32)(26,33)(27,28)(29,34)(30,35);(20,22)(21,26)(23,30)(24,31)(25,33)(27,34)(28,29)(32,35)551 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12711, C19×#12713, C19×#12716, … |
| maximal normal subgroup of | C19×#12711, C19×#12713, C19×#12716, … |
| maximal quotient of | C19×#8322, C19×#8324, C19×#8325, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 527);