Finite Group DatabasebetaFinite Group Databasebeta| order | 1998 |
| isoclinism | isoclinic class of #66526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C27 · Schur multiplier (H2) = C1 |
| direct product | C2×#11758603 |
| derived, Sylow | C37 ⋊ C2×C27 |
| Hall | C2×C37 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #66526 |
| commutator, hypocenter | C37 | C2×C27 |
| Frattini | C3 | C2×#66526 |
| Fitting, socle, prime radical | C2×C3×C37 | C9 |
| cosocle | #66524 | C2×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 66 |
| transitive degree | μt(G) = 1998 |
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1998, 8);