Finite Group DatabasebetaFinite Group Databasebeta| order | 15162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C192 ⋊ C2×C3 |
| Hall | #21439061 ⋊ C2 |
| Hall | C7×C19⋊D19 ⋊ C3 |
| Hall | C19⋊D19 ⋊ ΓL(1,𝔽8) |
| Sylow | C192 ⋊ C2×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ #14524206 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C192 | C2×C3 |
| LCS | G ▷ C7×C192 | |
| UCS | C1 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2527 |
Polycyclic presentation:
2,3,7,19^2|d^a=d^18,e^a=e^18,c^b=c^2,d^b=d^11,e^b=e^11430 conjugacy classes — view the full character table.
| maximal subgroup of | #44476567, #44476581, #44476591, … |
| maximal normal subgroup of | #44476567, #44476581, #44476591, … |
| maximal quotient of | #44476516, C2×#29503124 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15162, 59);