Finite Group DatabasebetaFinite Group Databasebeta| order | 8036 |
| isoclinism | isoclinic class of #5997 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C7 |
| direct product | C41×#5997 |
| Fitting, socle, Hall | C72×C41 ⋊ C4 |
| derived, Sylow | C72 ⋊ C4×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | #5997 |
| commutator, hypocenter | C72 | C4×C41 |
| Frattini | C1 | G |
| Fitting, socle | C72×C41 | C4 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C41 | |
28 conjugacy classes of subgroups.
656 conjugacy classes — view the full character table.
| maximal subgroup of | C41×#10596885, C41×#5997⋊C3, C3×C41×#5997, … |
| maximal normal subgroup of | C41×#5997⋊C3, C3×C41×#5997 |
| maximal quotient of | C3×C41×#5997, C41×C3⋊#5997 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8036, 27);