Finite Group DatabasebetaFinite Group Databasebeta| order | 11468 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×#6923 |
| Fitting, socle, Hall | C47×C61 ⋊ C4 |
| derived, Sylow | C61 ⋊ C4×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | #6923 |
| commutator, hypocenter | C61 | C4×C47 |
| Frattini | C1 | G |
| Fitting, socle | C47×C61 | C4 |
| prime radical | C47×D61 | C2 |
| cosocle | D61 | C2×C47 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C47 | |
12 conjugacy classes of subgroups.
893 conjugacy classes — view the full character table.
| maximal subgroup of | C47×#6923⋊C3, C3×C47×#6923, C47×C3⋊#6923 |
| maximal normal subgroup of | C47×#6923⋊C3, C3×C47×#6923 |
| maximal quotient of | C3×C47×#6923, C47×C3⋊#6923 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11468, 6);