Finite Group DatabasebetaFinite Group Databasebeta| order | 19178 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C223 · Schur multiplier (H2) = C1 |
| direct product | D43×C223 |
| unambiguous semidirect product | C43⋊(C2×C223) |
| Fitting, socle, Hall | C43×C223 ⋊ C2 |
| derived, Sylow | C43 ⋊ C2×C223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C223 | D43 |
| commutator, cosocle, hypocenter | C43 | C2×C223 |
| Frattini | C1 | G |
| Fitting, socle | C43×C223 | C2 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C223 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9589 |
5129 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D223, C2×D43×C223 |
| maximal normal subgroup of | D43×D223, C2×D43×C223 |
| maximal quotient of | Dic43×C223, C2×D43×C223 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19178, 1);