Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C43 |
| direct product | C19×#2785 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| prime radical | C22×D4×C19 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
428 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 176 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) = 1216 |
A minimal faithful permutation representation — 4 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)(23,26,27,25)(28,29)(30,33)(31,32)(34,35)(37,38)(41,42);(21,22)(23,27)(29,31)(33,34)(36,37,40,38)(39,42,43,41);(20,22,24,21)(23,26,27,25)(28,30,32,35)(29,33,31,34)(36,38,40,37)(39,42,43,41);(20,23,24,27)(21,25,22,26)(28,31,32,29)(30,34,35,33)(36,39)(37,41)(38,42)(40,43)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12145, C19×#12239, C19×#36796, … |
| maximal normal subgroup of | C19×#12145, C19×#12239, C19×#36796, … |
| maximal quotient of | C19×#14399, C19×#14476, C19×#14589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1517);