Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×Dic51 |
| unambiguous semidirect product | C3⋊(C72×Dic17) |
| derived, Hall | C3×C17 ⋊ C4×C72 |
| Hall | C3×C72×C17 ⋊ C4 |
| Hall | C72×C17 ⋊ Dic3 |
| Hall | C3×C72 ⋊ Dic17 |
| Sylow | C17 ⋊ C72×Dic3 |
| Sylow | C3 ⋊ C72×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | D51 |
| commutator, hypocenter | C3×C17 | C4×C72 |
| Frattini | C2 | C72×D51 |
| Fitting, socle, prime radical | C2×C3×C72×C17 | C2 |
| cosocle | C2×C3×C17 | C2×C72 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2×C72 | |
120 conjugacy classes of subgroups.
2646 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×Dic153, C7×ΓL(1,𝔽8)×Dic51, #3861×Dic51, … |
| maximal normal subgroup of | C7×ΓL(1,𝔽8)×Dic51, #3861×Dic51, #3862×Dic51, … |
| maximal quotient of | C72×Dic153, C72×C3⋊Dic51, C3×C72×Dic51 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 70);