Finite Group DatabasebetaFinite Group Databasebeta| order | 33027 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C101 · Schur multiplier (H2) = C1 |
| direct product | C101×C109⋊C3 |
| unambiguous semidirect product | C109⋊(C3×C101) |
| unambiguous semidirect product | (C101×C109)⋊C3 |
| Fitting, socle, Hall | C101×C109 ⋊ C3 |
| derived, Sylow | C109 ⋊ C3×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | C109⋊C3 |
| commutator, cosocle, hypocenter | C109 | C3×C101 |
| Frattini | C1 | G |
| Fitting, socle | C101×C109 | C3 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C101 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11009 |
3939 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33027, 1);