Finite Group DatabasebetaFinite Group Databasebeta| order | 18810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5×C19 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×C19×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5×C19 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C32×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C11×C19 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C32×C5×C19 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9405 |
5985 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C5×D11×D19, C32×D5×C19×D11, C32×D11×D95, … |
| maximal normal subgroup of | C32×C5×D11×D19, C32×D5×C19×D11, C32×D11×D95, … |
| maximal quotient of | C32×C5×C19×Dic11, C2×C32×C5×C19×D11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18810, 107);