Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C7 |
| direct product | C5×C13×C3⋊(C7⋊D7) |
| unambiguous semidirect product | C3⋊(C5×C13×C7⋊D7) |
| unambiguous semidirect product | C7⋊(C5×C13×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C13 | C3⋊(C7⋊D7) |
| commutator, cosocle, hypocenter | C3×C72 | C2×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72×C13 | C2 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C5×C13 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9555 |
4875 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C13×D7×D21, C5×D91⋊D21, C5×D13×C3⋊(C7⋊D7), … |
| maximal normal subgroup of | C5×C13×D7×D21, C5×D91⋊D21, C5×D13×C3⋊(C7⋊D7), … |
| maximal quotient of | C5×C13×C3⋊(C7⋊Dic7), C2×C5×C13×C3⋊(C7⋊D7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 185);