Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#551 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C13 |
| prime radical | C13×#120 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
248 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,21)(16,22,23,19)(18,20,25,27)(24,28,29,26);(14,16,18,24)(15,19,20,26)(17,23,25,29)(21,22,27,28);(15,20)(19,26)(21,27)(22,28);(16,23)(19,22)(24,29)(26,28)325 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1552);