Finite Group DatabasebetaFinite Group Databasebeta| order | 12220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C47⋊#261 |
| unambiguous semidirect product | C47⋊(C5×#261) |
| Fitting, socle, Hall | C5×C13×C47 ⋊ C4 |
| derived, Hall | C13×C47 ⋊ C4×C5 |
| Hall | C5×C47 ⋊ #261 |
| Hall | C5×C13 ⋊ Dic47 |
| Sylow | C47 ⋊ C5×#261 |
| Sylow | C13 ⋊ C5×Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C47⋊#261 |
| commutator, hypocenter | C13×C47 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C47 | C4 |
| prime radical | C5×D13×C47 | C2 |
| cosocle | D13×C47 | C2×C5 |
| LCS | G ▷ C13×C47 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
955 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C47⋊AGL(1,𝔽13), C3×C5×C47⋊#261, C5×C3⋊(C47⋊#261) |
| maximal normal subgroup of | C5×C47⋊AGL(1,𝔽13), C3×C5×C47⋊#261 |
| maximal quotient of | C3×C5×C47⋊#261, C5×C3⋊(C47⋊#261) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12220, 11);