Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×C5⋊(D13⋊C3) |
| unambiguous semidirect product | C5⋊(C72×D13⋊C3) |
| unambiguous semidirect product | (C13⋊C3)⋊(C72×D5) |
| unambiguous semidirect product | D65⋊(C3×C72) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C5⋊(D13⋊C3) |
| commutator, cosocle, hypocenter | C5×C13 | C2×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C13 | C2×C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C72 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3185 |
1078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×#63122⋊C3, C72×#63121⋊C3, C7×#19129748, … |
| maximal normal subgroup of | C72×#63122⋊C3, C72×#63121⋊C3, C7×#19129748, … |
| maximal quotient of | C72×Dic65⋊C3, C2×C72×C5⋊(D13⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 105);