Finite Group DatabasebetaFinite Group Databasebeta| order | 5700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊D95 |
| Fitting, socle, derived, Hall | C3×C52×C19 ⋊ C22 |
| Hall | C52×C19 ⋊ C2×D3 |
| Hall | C3×C52 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ D52 |
| Sylow | C52 ⋊ D3×D19 |
| Sylow | C19 ⋊ D15⋊D5 |
| Sylow | C3 ⋊ D5×D95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C19 | C22 |
| LCS | G ▷ C3×C52×C19 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5^2,19|d^a=d^4,e^a=e^4,f^a=f^18,c^b=c^2,d^b=d^4435 conjugacy classes — view the full character table.
| maximal subgroup of | #90646⋊D19, D45⋊D95, D15⋊(C5⋊(D19⋊C3)), … |
| maximal normal subgroup of | D15⋊(C5⋊(D19⋊C3)), C3×D15⋊D95 |
| maximal quotient of | D45⋊D95, C3×D15⋊D95, #30685919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5700, 146);