Finite Group DatabasebetaFinite Group Databasebeta| order | 19110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#16838413 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #16838413 |
| commutator, cosocle, hypocenter | C13×C49 | C2×C3×C5 |
| Frattini | C7 | C5×#10587716 |
| Fitting | C5×C13×C49 | C2×C3 |
| socle | C5×C7×C13 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C13×C49 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3185 |
680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#21439464, C5×#16838413⋊C2, C5×#21439461, … |
| maximal normal subgroup of | C5×#21439464, C5×#16838413⋊C2, C5×#21439461, … |
| maximal quotient of | C5×#21439437, C2×C5×#16838413 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19110, 23);