Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#471 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #121 |
| commutator, Frattini, cosocle | C2×C4 | C23×C13 |
| prime radical | C13×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ G | |
104 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(15,19)(16,22)(17,25)(21,27)(23,24)(26,28);(14,15,17,19,18,21,25,27)(16,20,23,26,24,29,22,28);(14,16)(15,20)(17,23)(18,24)(19,26)(21,29)(22,25)(27,28)208 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 972);