Finite Group DatabasebetaFinite Group Databasebeta| order | 11468 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊#6923 |
| Fitting, socle, derived, Hall | C47×C61 ⋊ C4 |
| Sylow | C61 ⋊ Dic47 |
| Sylow | C47 ⋊ #6923 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C47×C61 | C4 |
| prime radical, cosocle | C47×D61 | C2 |
| LCS | G ▷ C47×C61 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,47,61|a^2=b,c^a=c^46,d^a=d^50,d^b=d^60755 conjugacy classes — view the full character table.
| maximal subgroup of | C47⋊(#6923⋊C3), C3×C47⋊#6923, C3⋊(C47⋊#6923) |
| maximal normal subgroup of | C47⋊(#6923⋊C3), C3×C47⋊#6923 |
| maximal quotient of | C3×C47⋊#6923, C3⋊(C47⋊#6923) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11468, 7);