Finite Group DatabasebetaFinite Group Databasebeta| order | 15738 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#21463501 |
| Fitting, socle, Hall | C2×C43×C61 ⋊ C3 |
| derived, Hall | C43×C61 ⋊ C2×C3 |
| Hall | C2×C61 ⋊ C43⋊C3 |
| Hall | C2×C43 ⋊ C61⋊C3 |
| Sylow | C61 ⋊ C2×C43⋊C3 |
| Sylow | C43 ⋊ C2×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #21463501 |
| commutator, cosocle, hypocenter | C43×C61 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C43×C61 | C3 |
| LCS | G ▷ C43×C61 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5246 |
1754 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#21463501, #44538340, #44538344, … |
| maximal normal subgroup of | C4×#21463501, #44538340, #44538344, … |
| maximal quotient of | C4×#21463501, C22×#21463501 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15738, 5);