Finite Group DatabasebetaFinite Group Databasebeta| order | 8601 |
| isoclinism | isoclinic class of C61⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×C61⋊C3 |
| unambiguous semidirect product | C61⋊(C3×C47) |
| unambiguous semidirect product | (C47×C61)⋊C3 |
| Fitting, socle, Hall | C47×C61 ⋊ C3 |
| derived, Sylow | C61 ⋊ C3×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | C61⋊C3 |
| commutator, hypocenter | C61 | C3×C47 |
| Frattini | C1 | G |
| Fitting, socle | C47×C61 | C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C47 | |
8 conjugacy classes of subgroups.
1081 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C47×C61⋊C3, C47×D61⋊C3, D47×C61⋊C3, … |
| maximal normal subgroup of | C2×C47×C61⋊C3, C47×D61⋊C3, D47×C61⋊C3, … |
| maximal quotient of | C2×C47×C61⋊C3, C47×C61⋊C9, C3×C47×C61⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8601, 1);