Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(Dic11⋊C25) |
| unambiguous semidirect product | (C11⋊C25)⋊Dic7 |
| unambiguous semidirect product | Dic77⋊C25 |
| derived, Hall | C7×C11 ⋊ C4×C25 |
| Hall | C7×C11⋊C25 ⋊ C4 |
| Hall | Dic77 ⋊ C25 |
| Hall | C11⋊C25 ⋊ Dic7 |
| Sylow | C11 ⋊ C25×Dic7 |
| Sylow | C7 ⋊ Dic11⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C5 | C7⋊AGL(1,𝔽11) |
| commutator, hypocenter | C7×C11 | C4×C25 |
| Fitting, socle | C2×C5×C7×C11 | C2×C5 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C2×C5 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,11,2,5|a^2=e,b^5=f,c^a=c^6,d^a=d^10,d^b=d^4320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 4);