Finite Group DatabasebetaFinite Group Databasebeta| order | 2380 |
| isoclinism | isoclinic class of D35⋊D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D35⋊D17 |
| unambiguous semidirect product | D85⋊D7 |
| unambiguous semidirect product | D119⋊D5 |
| Fitting, socle, derived, Hall | C5×C7×C17 ⋊ C22 |
| Hall | C7×C17 ⋊ C2×D5 |
| Hall | C5×C17 ⋊ C2×D7 |
| Hall | C5×C7 ⋊ C2×D17 |
| Sylow | C17 ⋊ D5×D7 |
| Sylow | C7 ⋊ D5×D17 |
| Sylow | C5 ⋊ D7×D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C17 | C22 |
| LCS | G ▷ C5×C7×C17 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 595 |
Polycyclic presentation:
2^2,5,7,17|d^a=d^6,e^a=e^16,c^b=c^4,d^b=d^6172 conjugacy classes — view the full character table.
| maximal subgroup of | D119⋊D25, C5×D35⋊D17, D119⋊(C5⋊D5), … |
| maximal normal subgroup of | C5×D35⋊D17, C7×D35⋊D17, C11×D35⋊D17, … |
| maximal quotient of | D119⋊D25, C5×D35⋊D17, D119⋊(C5⋊D5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2380, 28);