Finite Group DatabasebetaFinite Group Databasebeta| order | 33558 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D2397 |
| unambiguous semidirect product | C3⋊(C7×D799) |
| unambiguous semidirect product | C17⋊(C7×D141) |
| unambiguous semidirect product | C47⋊(C7×D51) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D2397 |
| commutator, cosocle, hypocenter | C3×C17×C47 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C17×C47 | C2 |
| LCS | G ▷ C3×C17×C47 | |
| UCS | C1 ◁ C7 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16779 |
8400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33558, 13);