Finite Group DatabasebetaFinite Group Databasebeta| order | 15921 |
| isoclinism | isoclinic class of C61⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C29 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C29×C61 ⋊ C3 |
| derived, Sylow | C61 ⋊ C32×C29 |
| Hall | C29×C61 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C29 | C61⋊C3 |
| commutator, cosocle, hypocenter | C61 | C32×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C61 | C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C3×C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5307 |
2001 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C29×D61⋊C3, C3×C29⋊(D61⋊C3), C3×D29×C61⋊C3, … |
| maximal normal subgroup of | C3×C29×D61⋊C3, C3×C29⋊(D61⋊C3), C3×D29×C61⋊C3, … |
| maximal quotient of | C2×C3×C29×C61⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15921, 4);