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 | C61×D43 ⋊ C3 |
| Hall | D43 ⋊ C61⋊C3 |
| Sylow | C61 ⋊ D43⋊C3 |
| Sylow | C43 ⋊ C2×C61⋊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|c^a=c^42,c^b=c^36,d^b=d^13473 conjugacy classes — view the full character table.
| maximal subgroup of | #30628680⋊C2, C2×#30628684 |
| maximal normal subgroup of | #30628680⋊C2, C2×#30628684 |
| maximal quotient of | #44538344, C2×#30628684 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15738, 20);