Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C29 |
| unambiguous semidirect product | #16809854⋊C3 |
| derived, Sylow | C292 ⋊ C3×C4 |
| Hall | #16809854 ⋊ C3 |
| Hall | C292⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C29⋊D29)⋊C3 |
| commutator, hypocenter | C292 | C3×C4 |
| Fitting, socle, cosocle | C2×C292 | C2×C3 |
| prime radical | C2×C292⋊C3 | C2 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C2 | |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,29^2,2|a^2=e,c^a=c^28,d^a=d^28,c^b=c^8d^22,d^b=c^27d^20292 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#16809854⋊C3, C3⋊(#16809854⋊C3) |
| maximal normal subgroup of | C3×#16809854⋊C3 |
| maximal quotient of | #16809854⋊C9, C3×#16809854⋊C3, C3⋊(#16809854⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 15);