Finite Group DatabasebetaFinite Group Databasebeta| order | 37118 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C277 · Schur multiplier (H2) = C1 |
| direct product | D67×C277 |
| unambiguous semidirect product | C67⋊(C2×C277) |
| Fitting, socle, Hall | C67×C277 ⋊ C2 |
| derived, Sylow | C67 ⋊ C2×C277 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C277 | D67 |
| commutator, cosocle, hypocenter | C67 | C2×C277 |
| Frattini | C1 | G |
| Fitting, socle | C67×C277 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C277 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18559 |
9695 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37118, 1);