Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C7 |
| direct product | C3×C5×C7⋊D91 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | C7⋊D91 |
| commutator, cosocle, hypocenter | C72×C13 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72×C13 | C2 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3×C5 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9555 |
4800 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×#14579330, C3×C5×D7×D91, C3×C5×D13×C7⋊D7, … |
| maximal normal subgroup of | C3×C5×#14579330, C3×C5×D7×D91, C3×C5×D13×C7⋊D7, … |
| maximal quotient of | C3×C5×C7⋊Dic91, C2×C3×C5×C7⋊D91 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 196);