Finite Group DatabasebetaFinite Group Databasebeta| order | 8036 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×#4223 |
| Fitting, socle, Hall | C72×C41 ⋊ C4 |
| derived, Sylow | C41 ⋊ C4×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | #4223 |
| commutator, hypocenter | C41 | C4×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C41 | C4 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C72 | |
60 conjugacy classes of subgroups.
686 conjugacy classes — view the full character table.
| maximal subgroup of | C7×ΓL(1,𝔽8)×#4223, #3861×#4223, #3862×#4223, … |
| maximal normal subgroup of | C7×ΓL(1,𝔽8)×#4223, #3861×#4223, #3862×#4223, … |
| maximal quotient of | C3×C72×#4223, C72×C3⋊#4223 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8036, 19);