Finite Group DatabasebetaFinite Group Databasebeta| order | 9736 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1217 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19096454 |
| commutator, hypocenter | C1217 | C8 |
| Fitting, socle, prime radical | C2×C1217 | C4 |
| cosocle | Dic1217 | C2 |
| LCS | G ▷ C1217 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1217|a^2=b,b^2=c,d^a=d^78,d^b=d^1216616 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#23753593, #34085752, #34085753, … |
| maximal normal subgroup of | C2×#23753593, #34085752, #34085753, … |
| maximal quotient of | #34085747, C2×#23753593 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9736, 13);