Finite Group DatabasebetaFinite Group Databasebeta| order | 15026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D683 |
| Fitting, socle, Hall | C11×C683 ⋊ C2 |
| derived, Sylow | C683 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D683 |
| commutator, cosocle, hypocenter | C683 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C683 | C2 |
| LCS | G ▷ C683 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7513 |
3773 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D683, C2×C11×D683 |
| maximal normal subgroup of | D11×D683, C2×C11×D683 |
| maximal quotient of | C11×Dic683, C2×C11×D683 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15026, 4);