Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#546 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
334 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,22,23)(20,24,25,21);(19,23)(21,24);(14,15)(16,17)(18,20)(19,21)(22,25)(23,24);(18,21)(19,20)(22,24)(23,25)325 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1547);