Finite Group DatabasebetaFinite Group Databasebeta| order | 15134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊AGL(1,𝔽47) |
| unambiguous semidirect product | D329⋊C23 |
| unambiguous semidirect product | (C47⋊C23)⋊D7 |
| Fitting, socle, derived, Hall | C7×C47 ⋊ C2×C23 |
| Hall | C7×C47⋊C23 ⋊ C2 |
| Hall | C47⋊C23 ⋊ D7 |
| Hall | D329 ⋊ C23 |
| Sylow | C47 ⋊ D7×C23 |
| Sylow | C7 ⋊ AGL(1,𝔽47) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C47 | C2×C23 |
| LCS | G ▷ C7×C47 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 329 |
Polycyclic presentation:
2,7,23,47|b^a=b^6,d^a=d^46,d^c=d^25122 conjugacy classes — view the full character table.
| maximal subgroup of | D7×AGL(1,𝔽47), C2×C7⋊AGL(1,𝔽47) |
| maximal normal subgroup of | D7×AGL(1,𝔽47), C2×C7⋊AGL(1,𝔽47) |
| maximal quotient of | C7⋊(Dic47⋊C23), C2×C7⋊AGL(1,𝔽47) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15134, 12);