Finite Group DatabasebetaFinite Group Databasebeta| order | 14415 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C312 ⋊ C3×C5 |
| Hall | C31×ΓL(1,𝔽32) ⋊ C3 |
| Hall | #15668333 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C312 | C3×C5 |
| LCS | G ▷ C312 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 465 |
Polycyclic presentation:
3,5,31^2|c^a=c^5,d^a=d^25,c^b=c^16127 conjugacy classes — view the full character table.
| maximal subgroup of | #43273809, #43273810, #43273818, … |
| maximal normal subgroup of | #43273809, #43273810, #43273818, … |
| maximal quotient of | C2×#28385708 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14415, 7);