Finite Group DatabasebetaFinite Group Databasebeta| order | 19118 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C79 · Schur multiplier (H2) = C11 |
| direct product | C79×C11⋊D11 |
| unambiguous semidirect product | C11⋊(D11×C79) |
| Fitting, socle, Hall | C112×C79 ⋊ C2 |
| derived, Sylow | C112 ⋊ C2×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | C11⋊D11 |
| commutator, cosocle, hypocenter | C112 | C2×C79 |
| Frattini | C1 | G |
| Fitting, socle | C112×C79 | C2 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C79 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9559 |
4898 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C79×#92150, C79⋊#92150, D112×C79, … |
| maximal normal subgroup of | C79×#92150, C79⋊#92150, D112×C79, … |
| maximal quotient of | C79×C11⋊Dic11, C2×C79×C11⋊D11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19118, 7);