Finite Group DatabasebetaFinite Group Databasebeta| order | 33306 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C61 · Schur multiplier (H2) = C1 |
| direct product | D7×C13⋊C3×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D7×C13⋊C3 |
| commutator, cosocle, hypocenter | C7×C13 | C2×C3×C61 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C61 | C2×C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C61 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5551 |
2135 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33306, 70);