Finite Group DatabasebetaFinite Group Databasebeta| order | 33852 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | C2×C31×D273 |
| unambiguous semidirect product | (C2×C3)⋊(C31×D91) |
| unambiguous semidirect product | (C2×C7)⋊(C31×D39) |
| unambiguous semidirect product | (C2×C13)⋊(C31×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D273 |
| commutator, cosocle, hypocenter | C3×C7×C13 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C13×C31 | C2 |
| LCS | G ▷ C3×C7×C13 | |
| UCS | C1 ◁ C2×C31 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16926 |
8556 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33852, 439);