Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×C13×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C13 | #3861 |
| commutator, cosocle, hypocenter | C72 | C2×C3×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72×C13 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C5×C13 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6370 |
2470 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C13×#10596874, C5×#21439526, C5×C13×#10596873, … |
| maximal normal subgroup of | C5×C13×#10596874, C5×#21439526, C5×C13×#10596873, … |
| maximal quotient of | C4×C5×C13×#3861, C22×C5×C13×#3861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 176);