Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C7 |
| direct product | C13⋊C3×C5⋊(C7⋊D7) |
| unambiguous semidirect product | C5⋊(C13⋊C3×C7⋊D7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C13 | C2×C3 |
| LCS | G ▷ C5×C72×C13 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3185 |
868 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50303810, C13⋊C3×#11758266, ((C13⋊C3)⋊D7)⋊D35, … |
| maximal normal subgroup of | #50303810, C13⋊C3×#11758266, ((C13⋊C3)⋊D7)⋊D35, … |
| maximal quotient of | C13⋊C3×C7⋊Dic35, C2×C13⋊C3×C5⋊(C7⋊D7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 166);