Finite Group DatabasebetaFinite Group Databasebeta| order | 4292 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C29×C37 ⋊ C4 |
| Sylow | C37 ⋊ #1181 |
| Sylow | C29 ⋊ Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C37 | C4 |
| prime radical, cosocle | C37×D29 | C2 |
| LCS | G ▷ C29×C37 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 66 |
| transitive degree | μt(G) = 1073 |
Polycyclic presentation:
2^2,29,37|a^2=b,c^a=c^17,d^a=d^36,c^b=c^28299 conjugacy classes — view the full character table.
| maximal subgroup of | #16864282⋊C3, C3×#16864282, C3⋊#16864282, … |
| maximal normal subgroup of | #16864282⋊C3, C3×#16864282, C5×#16864282, … |
| maximal quotient of | C3×#16864282, C3⋊#16864282, C5×#16864282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4292, 10);