Finite Group DatabasebetaFinite Group Databasebeta| order | 9282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊#10587717 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C13×C17 | C2×C3 |
| LCS | G ▷ C7×C13×C17 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,13,17|d^a=d^12,e^a=e^16,c^b=c^2,d^b=d^9288 conjugacy classes — view the full character table.
| maximal subgroup of | #32915469, #32915470, #10587721⋊D17, … |
| maximal normal subgroup of | #32915469, #32915470, #10587721⋊D17, … |
| maximal quotient of | #32915437, C2×C17⋊#10587717, C17⋊#13109897, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9282, 32);