Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C11⋊#1042) |
| unambiguous semidirect product | C11⋊(C7⋊#1042) |
| Fitting, socle, derived, Hall | C52×C7×C11 ⋊ C4 |
| Hall | C52×C11 ⋊ Dic7 |
| Hall | C52×C7 ⋊ Dic11 |
| Hall | C7×C11 ⋊ #1042 |
| Sylow | C52 ⋊ Dic77 |
| Sylow | C11 ⋊ C7⋊#1042 |
| Sylow | C7 ⋊ C11⋊#1042 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C7×C11 | C4 |
| LCS | G ▷ C52×C7×C11 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,7,11|a^2=b,c^a=c^2,d^a=d^4,e^a=e^6,f^a=f^10,c^b=c^4773 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 99);