Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q8×C13 ⋊ C2 |
| Sylow | C13 ⋊ #529 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D13 |
| commutator, socle, cosocle | C22×C13 | C24 |
| Frattini | C22 | C23×D13 |
| Fitting | C4×Q8×C13 | C2 |
| prime radical | #88149 | C2 |
| hypercenter | C4×Q8 | D13 |
| hypocenter | C13 | #529 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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^2=f,d^a=df,g^a=g^12,d^b=def148 conjugacy classes — view the full character table.
| maximal subgroup of | #13113243, #13113248, #13113295, … |
| maximal normal subgroup of | #13113243, #13113248, #13113295, … |
| maximal quotient of | #13117232, #13117277, #13117297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1251);