Finite Group DatabasebetaFinite Group Databasebeta| order | 33180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C79 · Schur multiplier (H2) = C1 |
| direct product | C5×C79×Dic21 |
| unambiguous semidirect product | C3⋊(C5×Dic7×C79) |
| unambiguous semidirect product | C7⋊(C5×Dic3×C79) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C79 | D21 |
| commutator, hypocenter | C3×C7 | C4×C5×C79 |
| Frattini | C2 | C5×D21×C79 |
| Fitting, socle, prime radical | C2×C3×C5×C7×C79 | C2 |
| cosocle | C2×C3×C7 | C2×C5×C79 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C5×C79 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33180 |
9480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33180, 15);