Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D5×C13⋊C3 |
| unambiguous semidirect product | C5⋊(C2×C72×C13⋊C3) |
| unambiguous semidirect product | (D5×C13)⋊(C3×C72) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D5×C13⋊C3 |
| commutator, cosocle, hypocenter | C5×C13 | C2×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C13 | C2×C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C72 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3185 |
1372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 106);