Finite Group DatabasebetaFinite Group Databasebeta| order | 15162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | D7⋊#11762246 |
| Fitting, socle, derived, Hall | C7×C192 ⋊ C2×C3 |
| Hall | C7⋊#11762246 ⋊ C2 |
| Hall | D7×C192 ⋊ C3 |
| Sylow | C192 ⋊ AGL(1,𝔽7) |
| Hall | D7 ⋊ #11762246 |
| Sylow | C7 ⋊ C2×#11762246 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C192 | C2×C3 |
| LCS | G ▷ C7×C192 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 399 |
Polycyclic presentation:
2,3,7,19^2|c^a=c^6,c^b=c^2,d^b=d^7,e^b=e^11607 conjugacy classes — view the full character table.
| maximal subgroup of | #44476585, #44476586, D7⋊#14524207, … |
| maximal normal subgroup of | #44476585, #44476586, D7⋊#14524207, … |
| maximal quotient of | Dic7⋊#11762246, C2×D7⋊#11762246 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15162, 51);