Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16809857⋊C3 |
| Fitting, socle, derived, Sylow | C292 ⋊ C3×C4 |
| Hall | #16809857 ⋊ C3 |
| Hall | C292⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C292 | C3×C4 |
| prime radical | (C29⋊D29)⋊C3 | C2 |
| cosocle | C29⋊D29 | C2×C3 |
| LCS | G ▷ C292 | |
| UCS | C1 | |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,29^2|a^2=c,d^a=d^17,e^a=e^17,d^b=d^8e^22,e^b=d^27e^20,d^c=d^28,e^c=e^2882 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#16809857⋊C3, C3⋊(#16809857⋊C3) |
| maximal normal subgroup of | C3×#16809857⋊C3 |
| maximal quotient of | #16809857⋊C9, C3×#16809857⋊C3, C3⋊(#16809857⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 25);