Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q8×C13 ⋊ C2 |
| Sylow | C13 ⋊ #519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D13 |
| commutator | C2×C13 | C23×C4 |
| Fitting | C4×Q8×C13 | C2 |
| socle, cosocle | C22×C13 | C24 |
| prime radical | C22×D13 | C23 |
| hypercenter | C4×Q8 | D13 |
| hypocenter | C13 | #519 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^6,13|b^2=f,c^2=f,d^2=e,d^a=df,g^a=g^12,c^b=cf154 conjugacy classes — view the full character table.
| maximal subgroup of | #13123672, #13123674, #13123676, … |
| maximal normal subgroup of | #13123672, #13123674, #13123676, … |
| maximal quotient of | #13117190, #13117200, #13117201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1243);