Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#462 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C13 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,22,25)(20,26,28,33)(21,29,31,24)(23,30,32,27);(14,15,16,17);(18,20,22,28)(19,23,25,32)(21,30,31,27)(24,33,29,26)247 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 963);