Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#16809850 |
| Fitting, derived, Hall | C3×C841 ⋊ C4 |
| Sylow | C841 ⋊ Dic3 |
| Sylow | C3 ⋊ #16809850 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C841 | C4 |
| Frattini | C29 | C3⋊#1181 |
| socle | C3×C29 | #1181 |
| prime radical, cosocle | C3×D841 | C2 |
| LCS | G ▷ C3×C841 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,29^2|a^2=b,d^29=e^14,c^a=c^2,d^a=d^17e,e^a=e^17,d^b=d^28e^15,e^b=e^28636 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#16809850, C3×C3⋊#16809850, C3⋊(C3⋊#16809850) |
| maximal normal subgroup of | C3×C3⋊#16809850 |
| maximal quotient of | C9⋊#16809850, C3×C3⋊#16809850, C3⋊(C3⋊#16809850) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 7);