Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D5×#14274254 |
| unambiguous semidirect product | C5⋊(C2×#14274254) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C13×C49 | C2×C3 |
| Frattini | C7 | D5×#63270 |
| socle | C5×C7×C13 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C5×C13×C49 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3185 |
860 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50303385, #50303389, #50303397, … |
| maximal normal subgroup of | #50303385, #50303389, #50303397, … |
| maximal quotient of | Dic5×#14274254, C2×D5×#14274254 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 35);