Finite Group DatabasebetaFinite Group Databasebeta| order | 15598 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D709 |
| unambiguous semidirect product | C709⋊(C2×C11) |
| Fitting, socle, Hall | C11×C709 ⋊ C2 |
| derived, Sylow | C709 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D709 |
| commutator, cosocle, hypocenter | C709 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C709 | C2 |
| LCS | G ▷ C709 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7799 |
3916 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#15667778, C11⋊#15667778, D11×D709, … |
| maximal normal subgroup of | C11×#15667778, C11⋊#15667778, D11×D709, … |
| maximal quotient of | C11×Dic709, C2×C11×D709 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15598, 2);