Finite Group DatabasebetaFinite Group Databasebeta| order | 33975 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C25 · Schur multiplier (H2) = C3 |
| direct product | C32×#16836849 |
| derived, Sylow | C151 ⋊ C32×C25 |
| Hall | C32×C151 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | C151⋊C5 |
| commutator, hypocenter | C151 | C32×C25 |
| Frattini | C5 | C32×C151⋊C5 |
| Fitting, socle, prime radical | C32×C5×C151 | C5 |
| cosocle | C5×C151 | C32×C5 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C32×C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33975 |
1575 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33975, 7);