Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C7 |
| direct product | C17×#10596885 |
| Fitting, socle, Hall | C72×C17 ⋊ Dic3 |
| derived, Hall | #3862 ⋊ C4×C17 |
| Hall | C17×#3862 ⋊ C4 |
| Sylow | C72 ⋊ Dic3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #10596885 |
| commutator, hypocenter | #3862 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C72×C17 | Dic3 |
| prime radical | C17×#64425 | C2 |
| cosocle | #64425 | C2×C17 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C17 | |
36 conjugacy classes of subgroups.
170 conjugacy classes — view the full character table.
| maximal subgroup of | C17×#10596885⋊C3, C3×C17×#10596885, C17×C3⋊#10596885 |
| maximal normal subgroup of | C17×#10596885⋊C3, C3×C17×#10596885 |
| maximal quotient of | C17×#13183544, C3×C17×#10596885, C17×C3⋊#10596885 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 108);