Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#458 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #120 |
| commutator, Frattini, cosocle | C23 | C23×C13 |
| prime radical | C13×H(5,𝔽2) | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C23×C13 ◁ G | |
160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,21)(16,19,23,26)(17,20,24,27)(22,28,29,25);(14,16)(15,19)(17,22)(18,23)(20,25)(21,26)(24,29)(27,28);(14,17)(15,20)(16,22)(18,24)(19,25)(21,27)(23,29)(26,28)208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 959);