Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#2112 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C23 |
| commutator | C22 | C22×C8×C19 |
| Frattini, cosocle | C2×C8 | C23×C19 |
| socle | C22×C19 | C22×C8 |
| prime radical | C24×C19 | C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ G | |
260 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,26,30,27,31,32,37,28,29,33,35,34,36,38,39);(21,23);(25,29)(30,35)(31,36)(37,39)1064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#7184, C19×#7185, C19×#7200, … |
| maximal normal subgroup of | C19×#7184, C19×#7185, C19×#7200, … |
| maximal quotient of | C19×#11418, C19×#11440, C19×#11460, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 844);