Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#16809857 |
| Fitting, socle, derived, Hall | C3×C292 ⋊ C4 |
| Sylow | C292 ⋊ Dic3 |
| Sylow | C3 ⋊ #16809857 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C292 | C4 |
| prime radical, cosocle | C3×C29⋊D29 | C2 |
| LCS | G ▷ C3×C292 | |
| UCS | C1 | |
192 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,29^2|a^2=b,c^a=c^2,d^a=d^17,e^a=e^17,d^b=d^28,e^b=e^28636 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#16809857, C3⋊(#16809857⋊C3), C3×C3⋊#16809857, … |
| maximal normal subgroup of | C3⋊(#16809857⋊C3), C3×C3⋊#16809857 |
| maximal quotient of | C9⋊#16809857, C3×C3⋊#16809857, C3⋊(C3⋊#16809857) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 35);