Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | D5×C13×#3861 |
| unambiguous semidirect product | C5⋊(C2×C13×#3861) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D5×#3861 |
| commutator, cosocle, hypocenter | C5×C72 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C13 | C2×C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C13 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3185 |
988 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×AGL(1,𝔽5)×#3861, #3861×#63120, C13×#15668765, … |
| maximal normal subgroup of | C13×AGL(1,𝔽5)×#3861, #3861×#63120, C13×#15668765, … |
| maximal quotient of | C13×Dic5×#3861, C2×D5×C13×#3861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 149);