Finite Group DatabasebetaFinite Group Databasebeta| order | 33180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1659 |
| unambiguous semidirect product | C3⋊(C5×Dic553) |
| unambiguous semidirect product | C7⋊(C5×Dic237) |
| unambiguous semidirect product | C79⋊(C5×Dic21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1659 |
| commutator, hypocenter | C3×C7×C79 | C4×C5 |
| Frattini | C2 | C5×D1659 |
| Fitting, socle, prime radical | C2×C3×C5×C7×C79 | C2 |
| cosocle | C2×C3×C7×C79 | C2×C5 |
| LCS | G ▷ C3×C7×C79 | |
| UCS | C1 ◁ C2×C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33180 |
8310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33180, 16);