Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#1591 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×D4 |
| commutator | C2×C4 | C22×C4×C19 |
| Frattini, cosocle | C42 | C23×C19 |
| socle, prime radical | C22×C19 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C4×C8×C19 ◁ G | |
152 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,22,23,25,27,26)(28,29,32,35)(30,36,38,43)(31,39,41,34)(33,40,42,37);(21,25)(22,26)(28,30,32,38)(29,33,35,42)(31,40,41,37)(34,43,39,36);(20,22,24,25,23,26,27,21)836 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#7073, C19×#7075, C19×#12070, … |
| maximal normal subgroup of | C19×#7073, C19×#7075, C19×#12070, … |
| maximal quotient of | C19×#8207, C19×#8282, C19×#8848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 323);