Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#2822 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
380 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(25,26)(29,30)(32,33,37,39)(34,40,42,35)(36,38,46,47)(41,45,44,43);(21,23)(24,25,28,26)(27,29,31,30)(32,34,37,42)(33,35,39,40)(36,44,46,41)(38,45,47,43);(20,21)(22,23)(24,26,28,25)(27,29,31,30)(32,35)(33,34)(36,45)(37,40)(38,44)(39,42)(41,47)(43,46);(24,27,28,31)(25,29,26,30)(32,36,37,46)(33,38,39,47)(34,41,42,44)(35,43,40,45)494 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#10080, C19×#10084, C19×#10087, … |
| maximal normal subgroup of | C19×#10080, C19×#10084, C19×#10087, … |
| maximal quotient of | C19×#14629, C19×#14631, C19×#14634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1554);