Finite Group DatabasebetaFinite Group Databasebeta| order | 11468 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C47 · Schur multiplier (H2) = C2 |
| direct product | C2×C47×D61 |
| unambiguous semidirect product | C61⋊(C22×C47) |
| unambiguous semidirect product | (C2×C61)⋊(C2×C47) |
| Fitting, socle | C2×C47×C61 ⋊ C2 |
| derived, Sylow | C61 ⋊ C22×C47 |
| Hall | C47×C61 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C47 | D61 |
| commutator, cosocle, hypocenter | C61 | C22×C47 |
| Frattini | C1 | G |
| Fitting, socle | C2×C47×C61 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C47 | |
20 conjugacy classes of subgroups.
3008 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C47×D61⋊C3, D3×C47×D61, C2×C3×C47×D61, … |
| maximal normal subgroup of | C2×C47×D61⋊C3, C2×C3×C47×D61 |
| maximal quotient of | D3×C47×D61, C2×C3×C47×D61, C2×C47×D183 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11468, 11);