Finite Group DatabasebetaFinite Group Databasebeta| order | 8036 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊(C7⋊#4223) |
| Fitting, socle, derived, Hall | C72×C41 ⋊ C4 |
| Sylow | C72 ⋊ #4223 |
| Sylow | C41 ⋊ C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C41 | C4 |
| LCS | G ▷ C72×C41 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7^2,41|a^2=b,c^a=c^6,d^a=d^6,e^a=e^32,e^b=e^40542 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊(C7⋊#4223), #37563092, #37563105, … |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊(C7⋊#4223), #37563092, #37563105, … |
| maximal quotient of | C3×C7⋊(C7⋊#4223), C3⋊(C7⋊(C7⋊#4223)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8036, 22);