Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #19097943⋊C2 |
| unambiguous semidirect product | ((C29⋊D29)⋊C3)⋊C2 |
| Fitting, socle, Sylow | C292 ⋊ C2×D3 |
| derived, Hall | C292⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C292⋊C3 | C22 |
| Fitting, socle | C292 | C2×D3 |
| LCS | G ▷ C292⋊C3 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,29^2|c^a=c^2,d^a=d^20e^15,e^a=d^14e^9,c^b=c^2,d^b=d^9e^14,e^b=d^15e^20,d^c=d^8e^14,e^c=de^20118 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#19097943⋊C2, #19097943⋊D3, ((C29⋊D29)⋊C3)⋊D3 |
| maximal normal subgroup of | C3×#19097943⋊C2 |
| maximal quotient of | #29502829⋊C2, C3×#19097943⋊C2, #19097943⋊D3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 23);