Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#1638 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C19 |
| prime radical | C2×D4×C19 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ G | |
194 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 68 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 — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,28)(22,29,31,34)(23,27,24,32)(26,33,35,30)(36,37,41,45)(38,46,49,50)(39,44,40,43)(42,48,51,47);(20,22)(21,26)(23,30)(24,33)(25,31)(27,34)(28,35)(29,32)(36,38,41,49)(37,42,45,51)(39,48,40,47)(43,50,44,46);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(37,43)(39,40)(42,50)(44,45)(46,51)(47,48)494 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C19×#1638, C19×#18494, C19×#18521, … |
| maximal normal subgroup of | C2×C19×#1638, C19×#18494, C19×#18521, … |
| maximal quotient of | C19×#7765, C19×#7767, C19×#7773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 370);