Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | Aut(G) order 4620000 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3850 |
| direct product | C2×D1925 |
| unambiguous semidirect product | (C2×C7)⋊D275 |
| unambiguous semidirect product | (C2×C11)⋊D175 |
| unambiguous semidirect product | (C2×C25)⋊D77 |
| Fitting | C2×C7×C11×C25 ⋊ C2 |
| derived, Hall | C7×C11×C25 ⋊ C22 |
| Hall | C11×C25 ⋊ C2×D7 |
| Hall | C7×C25 ⋊ C2×D11 |
| Hall | C7×C11 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×D77 |
| Sylow | C11 ⋊ C2×D175 |
| Sylow | C7 ⋊ C2×D275 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1925 |
| commutator, hypocenter | C7×C11×C25 | C22 |
| Frattini | C5 | C2×D385 |
| Fitting | C2×C7×C11×C25 | C2 |
| socle | C2×C5×C7×C11 | D5 |
| LCS | G ▷ C7×C11×C25 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
1928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11⋊(ΓL(1,𝔽8)⋊D25), D3×D1925, C2×C3×D1925, … |
| maximal normal subgroup of | C2×C11⋊(ΓL(1,𝔽8)⋊D25), C2×C3×D1925, D7700 |
| maximal quotient of | D3×D1925, C2×C3×D1925, C2×D5775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 36);