Finite Group DatabasebetaFinite Group Databasebeta| order | 35204 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic677⋊C13 |
| derived, Sylow | C677 ⋊ C4×C13 |
| Hall | C677⋊C13 ⋊ C4 |
| Hall | Dic677 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D677⋊C13 |
| commutator, hypocenter | C677 | C4×C13 |
| Fitting, socle, cosocle | C2×C677 | C2×C13 |
| prime radical | C2×C677⋊C13 | C2 |
| LCS | G ▷ C677 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2708 |
Polycyclic presentation:
2,13,677,2|a^2=d,c^a=c^676,c^b=c^362104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35204, 2);