Finite Group DatabasebetaFinite Group Databasebeta| order | 22018 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C109 · Schur multiplier (H2) = C1 |
| direct product | C109×D101 |
| unambiguous semidirect product | C101⋊(C2×C109) |
| Fitting, socle, Hall | C101×C109 ⋊ C2 |
| derived, Sylow | C101 ⋊ C2×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C109 | D101 |
| commutator, cosocle, hypocenter | C101 | C2×C109 |
| Frattini | C1 | G |
| Fitting, socle | C101×C109 | C2 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C109 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11009 |
5668 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22018, 1);