Finite Group DatabasebetaFinite Group Databasebeta| order | 7708 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊#4223 |
| Fitting, socle, derived, Hall | C41×C47 ⋊ C4 |
| Sylow | C47 ⋊ #4223 |
| Sylow | C41 ⋊ Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C41×C47 | C4 |
| LCS | G ▷ C41×C47 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,41,47|a^2=b,c^a=c^32,d^a=d^46,c^b=c^40520 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C47⋊#4223, C3⋊(C47⋊#4223), C47⋊(#4223⋊C5), … |
| maximal normal subgroup of | C3×C47⋊#4223, C47⋊(#4223⋊C5), C5×C47⋊#4223 |
| maximal quotient of | C3×C47⋊#4223, C3⋊(C47⋊#4223), C5×C47⋊#4223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7708, 7);