Finite Group DatabasebetaFinite Group Databasebeta| order | 4292 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C37 · Schur multiplier (H2) = C2 |
| direct product | C2×C37×D29 |
| unambiguous semidirect product | C29⋊(C22×C37) |
| unambiguous semidirect product | (C2×C29)⋊(C2×C37) |
| Fitting, socle | C2×C29×C37 ⋊ C2 |
| derived, Sylow | C29 ⋊ C22×C37 |
| Hall | C29×C37 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | D29 |
| commutator, cosocle, hypocenter | C29 | C22×C37 |
| Frattini | C1 | G |
| Fitting, socle | C2×C29×C37 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C37 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2146 |
1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D29×C37⋊C3, D3×C37×D29, C2×C37×D87, … |
| maximal normal subgroup of | C2×D29×C37⋊C3, C2×C3×C37×D29, C2×C5×C37×D29, … |
| maximal quotient of | D3×C37×D29, C2×C37×D87, C2×C3×C37×D29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4292, 14);