Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊D5)⋊D77 |
| Fitting, socle, derived, Hall | C52×C7×C11 ⋊ C22 |
| Hall | C52×C11 ⋊ C2×D7 |
| Hall | C52×C7 ⋊ C2×D11 |
| Hall | C7×C11 ⋊ D52 |
| Sylow | C52 ⋊ C2×D77 |
| Sylow | C11 ⋊ (C5⋊D5)⋊D7 |
| Sylow | C7 ⋊ (C5⋊D5)⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C7×C11 | C22 |
| LCS | G ▷ C52×C7×C11 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,7,11|c^a=c^4,e^a=e^6,f^a=f^10,c^b=c^4,d^b=d^4548 conjugacy classes — view the full character table.
| maximal subgroup of | ((C5⋊D5)⋊C3)⋊D77, ((C5⋊D5)⋊D77)⋊C3, C3×(C5⋊D5)⋊D77, … |
| maximal normal subgroup of | ((C5⋊D5)⋊D77)⋊C3, C3×(C5⋊D5)⋊D77 |
| maximal quotient of | C3×(C5⋊D5)⋊D77, #37528689, #37528694 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 115);