Finite Group DatabasebetaFinite Group Databasebeta| order | 18736 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D1171 |
| unambiguous semidirect product | C1171⋊C24 |
| unambiguous semidirect product | (C2×C1171)⋊C23 |
| Fitting, socle | C23×C1171 ⋊ C2 |
| derived, Sylow | C1171 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D1171 |
| commutator, cosocle, hypocenter | C1171 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C1171 | C2 |
| LCS | G ▷ C1171 | |
| UCS | C1 ◁ C23 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9368 |
4696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D1171, C2×(C2×D1171)⋊C4, #49154026, … |
| maximal normal subgroup of | C22⋊C4×D1171, C2×(C2×D1171)⋊C4, #49154026, … |
| maximal quotient of | C22×C4×D1171, C23×Dic1171, C2×D4×D1171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18736, 42);