Finite Group DatabasebetaFinite Group Databasebeta| order | 32300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | D323⋊(C5⋊D5) |
| Fitting, socle, derived, Hall | C52×C17×C19 ⋊ C22 |
| Hall | C52×C19 ⋊ C2×D17 |
| Hall | C52×C17 ⋊ C2×D19 |
| Hall | C17×C19 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ D17×D19 |
| Sylow | C19 ⋊ D17×C5⋊D5 |
| Sylow | C17 ⋊ D19×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C17×C19 | C22 |
| LCS | G ▷ C52×C17×C19 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8075 |
Polycyclic presentation:
2^2,5^2,17,19|e^a=e^16,f^a=f^18,c^b=c^4,d^b=d^4,e^b=e^162066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32300, 93);