Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3003 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#3038 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C19 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
584 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(25,29)(26,27)(30,31);(20,21,22,23);(24,25)(26,29)(27,31)(28,30);(24,26,28,27)(25,29,30,31)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#9173, C19×#9174, C19×#9318, … |
| maximal normal subgroup of | C19×#9173, C19×#9174, C19×#9318, … |
| maximal quotient of | C19×#19266, C19×#19267, C19×#19268, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1770);