Finite Group DatabasebetaFinite Group Databasebeta| order | 18537 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C167 · Schur multiplier (H2) = C1 |
| direct product | C37⋊C3×C167 |
| unambiguous semidirect product | C37⋊(C3×C167) |
| unambiguous semidirect product | (C37×C167)⋊C3 |
| Fitting, socle, Hall | C37×C167 ⋊ C3 |
| derived, Sylow | C37 ⋊ C3×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C167 | C37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C3×C167 |
| Frattini | C1 | G |
| Fitting, socle | C37×C167 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C167 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6179 |
2505 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C37⋊C3×C167, C37⋊C3×D167, C167×D37⋊C3, … |
| maximal normal subgroup of | C2×C37⋊C3×C167, C37⋊C3×D167, C167×D37⋊C3, … |
| maximal quotient of | C2×C37⋊C3×C167 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18537, 1);