Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#353 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #99 |
| commutator | C2×C4 | C2×C4×C13 |
| Frattini, cosocle | C2×D4 | C22×C13 |
| prime radical | C13×#127 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C13 ◁ C2×D4×C13 ◁ G | |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 104 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19,21,18)(17,20);(15,18)(16,21)(19,20)169 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 158);