Finite Group DatabasebetaFinite Group Databasebeta| order | 15162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#14524212 |
| Fitting, socle, Hall | C7×C192 ⋊ D3 |
| derived, Hall | C7×#11762246 ⋊ C2 |
| Hall | #11762246 ⋊ D7 |
| Sylow | C192 ⋊ D21 |
| Sylow | C7 ⋊ #14524212 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×#11762246 | C2 |
| Fitting, socle | C7×C192 | D3 |
| LCS | G ▷ C7×#11762246 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 266 |
Polycyclic presentation:
2,3,7,19^2|b^a=b^2,c^a=c^6,d^a=e,e^a=d,d^b=d^11,e^b=e^7459 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#14524212, #14524212⋊D7, #44476611, … |
| maximal normal subgroup of | D7×#14524212, #14524212⋊D7, #44476611, … |
| maximal quotient of | C7⋊#16864564, C2×C7⋊#14524212 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15162, 80);