Finite Group DatabasebetaFinite Group Databasebeta| order | 18130 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C5⋊(C7⋊D259) |
| unambiguous semidirect product | C7⋊D1295 |
| unambiguous semidirect product | C37⋊(C5⋊(C7⋊D7)) |
| Fitting, socle, derived, Hall | C5×C72×C37 ⋊ C2 |
| Hall | C72×C37 ⋊ D5 |
| Hall | C5×C72 ⋊ D37 |
| Hall | C5×C37 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D185 |
| Sylow | C37 ⋊ C5⋊(C7⋊D7) |
| Sylow | C5 ⋊ C7⋊D259 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C37 | C2 |
| LCS | G ▷ C5×C72×C37 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9065 |
Polycyclic presentation:
2,5,7^2,37|b^a=b^4,c^a=c^6,d^a=d^6,e^a=e^364534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49136415, #49136416, D7×D1295, … |
| maximal normal subgroup of | #49136415, #49136416, D7×D1295, … |
| maximal quotient of | C7⋊Dic1295, C2×C5⋊(C7⋊D259) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18130, 10);