Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#117 ⋊ C2 |
| Sylow | C13 ⋊ #529 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D13 |
| commutator, socle, cosocle | C22×C13 | C24 |
| Frattini | C22 | C23×D13 |
| Fitting | C13×#117 | C2 |
| prime radical | #88138 | C2 |
| hypercenter | #117 | D13 |
| hypocenter | C13 | #529 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^6,13|b^2=f,c^2=e,d^a=de,g^a=g^12,d^c=df148 conjugacy classes — view the full character table.
| maximal subgroup of | #13123807, #13123809, #13123817, … |
| maximal normal subgroup of | #13123807, #13123809, #13123817, … |
| maximal quotient of | #13117228, #13117273, #13117280, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1199);