Finite Group DatabasebetaFinite Group Databasebeta| order | 9282 |
| automorphism | Aut(G) order 10692864 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4641 |
| unambiguous semidirect product | C3⋊D1547 |
| unambiguous semidirect product | C7⋊D663 |
| unambiguous semidirect product | C13⋊D357 |
| unambiguous semidirect product | C17⋊D273 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C13×C17 | C2 |
| LCS | G ▷ C3×C7×C13×C17 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,13,17|b^a=b^2,c^a=c^6,d^a=d^12,e^a=e^162322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×D273, D13×D357, D21×D221, … |
| maximal normal subgroup of | D17×D273, D13×D357, D21×D221, … |
| maximal quotient of | Dic4641, C2×D4641, D13923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9282, 20);