Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, Hall | C72×C17 ⋊ C2×D3 |
| derived, Hall | C17×#3862 ⋊ C22 |
| Hall | #3862 ⋊ C2×D17 |
| Sylow | C72 ⋊ C2×D51 |
| Sylow | C17 ⋊ #64418⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C17×#3862 | C22 |
| Fitting, socle | C72×C17 | C2×D3 |
| LCS | G ▷ C17×#3862 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,17,7^2|c^a=c^2,d^a=d^16,e^a=e^4f,f^a=e^6f^3,e^b=e^6,f^b=f^6,e^c=e^2f^6,f^c=f^4131 conjugacy classes — view the full character table.
| maximal subgroup of | #23756202⋊C3, C3×#23756202, #44472781, … |
| maximal normal subgroup of | #23756202⋊C3, C3×#23756202 |
| maximal quotient of | #44472553, C3×#23756202, #44472781, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 105);