Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#131 ⋊ C2 |
| Sylow | C13 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D13 |
| commutator, socle | C2×C13 | C23×C4 |
| Fitting | C13×#131 | C2 |
| prime radical | #41×D13 | C2 |
| cosocle | C4×C13 | C24 |
| hypercenter | #131 | D13 |
| hypocenter | C13 | #568 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C4 ◁ #131 | |
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^6,13|d^2=e,e^2=f,d^a=df,g^a=g^12,c^b=cf154 conjugacy classes — view the full character table.
| maximal subgroup of | #13123741, #13123744, #13123748, … |
| maximal normal subgroup of | #13123741, #13123744, #13123748, … |
| maximal quotient of | #13123252, #13123262, #13123263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1421);