Finite Group DatabasebetaFinite Group Databasebeta| order | 15170 |
| isoclinism | isoclinic class of C41⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C37 · Schur multiplier (H2) = C1 |
| direct product | C2×C37×C41⋊C5 |
| unambiguous semidirect product | (C2×C41)⋊(C5×C37) |
| unambiguous semidirect product | (C2×C37×C41)⋊C5 |
| Fitting, socle, Hall | C2×C37×C41 ⋊ C5 |
| derived, Sylow | C41 ⋊ C2×C5×C37 |
| Hall | C37×C41 ⋊ C2×C5 |
| Hall | C2×C41 ⋊ C5×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | C41⋊C5 |
| commutator, cosocle, hypocenter | C41 | C2×C5×C37 |
| Frattini | C1 | G |
| Fitting, socle | C2×C37×C41 | C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C37 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3034 |
962 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C37×C41⋊C5, C37×Dic41⋊C5, Dic37×C41⋊C5, … |
| maximal normal subgroup of | C4×C37×C41⋊C5, C37×Dic41⋊C5, Dic37×C41⋊C5, … |
| maximal quotient of | C4×C37×C41⋊C5, C22×C37×C41⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15170, 2);