Finite Group DatabasebetaFinite Group Databasebeta| order | 555 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C37⋊C3 |
| unambiguous semidirect product | C37⋊(C3×C5) |
| unambiguous semidirect product | (C5×C37)⋊C3 |
| Fitting, socle, Hall | C5×C37 ⋊ C3 |
| derived, Sylow | C37 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C37 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 185 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D37⋊C3, D5×C37⋊C3, C5⋊(D37⋊C3), … |
| maximal normal subgroup of | C5×D37⋊C3, D5×C37⋊C3, C5⋊(D37⋊C3), … |
| maximal quotient of | C2×C5×C37⋊C3, C5×#66524, C3×C5×C37⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(555, 1);