Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C72×C17 ⋊ Dic3 |
| derived, Hall | C17×#3862 ⋊ C4 |
| Hall | #3862 ⋊ #595 |
| Sylow | C72 ⋊ C3⋊#595 |
| Sylow | C17 ⋊ #10596868 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C17×#3862 | C4 |
| Fitting, socle | C72×C17 | Dic3 |
| prime radical, cosocle | D17×#3862 | C2 |
| LCS | G ▷ C17×#3862 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,17,7^2|a^2=b,c^a=c^2,d^a=d^13,e^a=e^2f^3,f^a=e^6f^5,d^b=d^16,e^c=e^4f^4,f^c=f^2116 conjugacy classes — view the full character table.
| maximal subgroup of | #23756203⋊C3, C3×#23756203, C3⋊#23756203 |
| maximal normal subgroup of | #23756203⋊C3, C3×#23756203 |
| maximal quotient of | #44472554, C3×#23756203, C3⋊#23756203 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 106);