Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#563 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C13 |
| prime radical | C2×D4×C13 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
196 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,20)(22,23,27,25)(24,30,32,28)(26,33,35,29)(31,36,34,37);(15,18)(19,21)(22,24,27,32)(23,28,25,30)(26,34,35,31)(29,37,33,36);(14,15)(16,19)(17,18)(20,21)(22,25,27,23)(24,28,32,30)(26,33,35,29)(31,36,34,37);(14,16)(15,19)(17,20)(18,21)(22,26)(23,29)(24,31)(25,33)(27,35)(28,36)(30,37)(32,34)247 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1564);