Finite Group DatabasebetaFinite Group Databasebeta| order | 33300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| Fitting | C2×C3×C25×C37 ⋊ C2×C3 |
| derived, Hall | C25×C37 ⋊ C22×C32 |
| Hall | C3×C25×C37⋊C3 ⋊ C22 |
| Hall | C2×D925 ⋊ C32 |
| Hall | C3×C37⋊C3 ⋊ C2×D25 |
| Sylow | C37 ⋊ C2×C32×D25 |
| Sylow | C25 ⋊ C2×C3×D37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C25⋊(D37⋊C3) |
| commutator, cosocle, hypocenter | C25×C37 | C22×C32 |
| Frattini | C5 | C2×C3×C5⋊(D37⋊C3) |
| Fitting | C2×C3×C25×C37 | C2×C3 |
| socle | C2×C3×C5×C37 | C3×D5 |
| LCS | G ▷ C25×C37 | |
| UCS | C1 ◁ C2×C3 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5550 |
1152 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33300, 139);