Finite Group DatabasebetaFinite Group Databasebeta| order | 15738 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C43×C61 ⋊ C2×C3 |
| Hall | #21463501 ⋊ C2 |
| Hall | C43×D61 ⋊ C3 |
| Hall | D61 ⋊ C43⋊C3 |
| Sylow | C61 ⋊ C2×C43⋊C3 |
| Sylow | C43 ⋊ D61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C61 | C2×C3 |
| LCS | G ▷ C43×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2623 |
Polycyclic presentation:
2,3,43,61|d^a=d^60,c^b=c^36,d^b=d^13464 conjugacy classes — view the full character table.
| maximal subgroup of | #44538351, #30628680⋊C2, #44538357, … |
| maximal normal subgroup of | #44538351, #30628680⋊C2, #44538357, … |
| maximal quotient of | #44538340, C2×#30628680 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15738, 16);