Finite Group DatabasebetaFinite Group Databasebeta| order | 8036 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C49⋊#4223 |
| Fitting, derived, Hall | C41×C49 ⋊ C4 |
| Sylow | C49 ⋊ #4223 |
| Sylow | C41 ⋊ Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C41×C49 | C4 |
| Frattini | C7 | C7⋊#4223 |
| socle | C7×C41 | Dic7 |
| LCS | G ▷ C41×C49 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7,41,7|a^2=b,c^7=e^6,c^a=c^6e,d^a=d^32,e^a=e^6,d^b=d^40542 conjugacy classes — view the full character table.
| maximal subgroup of | (C49⋊C3)⋊#4223, C3×C49⋊#4223, C3⋊(C49⋊#4223) |
| maximal normal subgroup of | (C49⋊C3)⋊#4223, C3×C49⋊#4223 |
| maximal quotient of | C3×C49⋊#4223, C3⋊(C49⋊#4223) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8036, 7);