Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#3531 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C19 |
| socle | C22×C19 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ G | |
930 conjugacy classes of subgroups; only the 760 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 760 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 5 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,28)(23,27)(24,26)(25,29)(30,34)(31,33)(32,35)(36,37)(38,41)(39,46)(40,43)(42,48)(44,51)(45,50)(47,49);(20,22)(21,25)(23,30)(24,29)(26,28)(27,32)(31,35)(33,34)(36,38,40,45)(37,41,43,50)(39,47,48,44)(42,51,46,49);(22,29)(25,28)(30,35)(32,34)(36,39,40,48)(37,42,43,46)(38,44,45,47)(41,49,50,51);(21,26)(22,29)(27,33)(30,35)(37,43)(41,50)(42,46)(49,51);(20,23,24,31)(21,27,26,33)(22,30,29,35)(25,32,28,34)722 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#8505, C19×#18990, C19×#18991, … |
| maximal normal subgroup of | C19×#8505, C19×#18990, C19×#18991, … |
| maximal quotient of | C19×#34348, C19×#34350, C4×C19×#562, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 2263);