Finite Group DatabasebetaFinite Group Databasebeta| order | 7950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C53⋊#3874 |
| Fitting, socle, Hall | C52×C53 ⋊ D3 |
| derived, Hall | C53×C52⋊C3 ⋊ C2 |
| Hall | C52⋊C3 ⋊ D53 |
| Sylow | C53 ⋊ #3874 |
| Sylow | C52 ⋊ D159 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C53×C52⋊C3 | C2 |
| Fitting, socle | C52×C53 | D3 |
| LCS | G ▷ C53×C52⋊C3 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,53,5^2|b^a=b^2,c^a=c^52,d^a=d^2e,e^a=d^2e^3,d^b=d^2e^4,e^b=d^2e^2299 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊D53, ((C5⋊D5)⋊C3)⋊D53, D53×#3874, … |
| maximal normal subgroup of | #3874⋊D53, ((C5⋊D5)⋊C3)⋊D53, D53×#3874, … |
| maximal quotient of | #30629704, C2×C53⋊#3874, C53⋊#90646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7950, 11);