Finite Group DatabasebetaFinite Group Databasebeta| order | 9736 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C1217 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1217 | C8 |
| prime radical | D1217 | C4 |
| cosocle | #19096454 | C2 |
| LCS | G ▷ C1217 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1217|a^2=b,b^2=c,d^a=d^387,d^b=d^78,d^c=d^1216160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#23753595, #34085758 |
| maximal normal subgroup of | C2×#23753595, #34085758 |
| maximal quotient of | #34085756, C2×#23753595 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9736, 15);