Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#470 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C13 |
| prime radical | C23×C13 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,22,25)(20,26,28,33)(21,30,27,24)(23,31,32,29);(18,20,27,31,22,28,21,29)(19,23,30,33,25,32,24,26);(15,17)(20,28)(23,32)(26,33)(29,31)208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 971);