Finite Group DatabasebetaFinite Group Databasebeta| order | 6975 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C31⋊C9)⋊C25 |
| unambiguous semidirect product | (C31⋊C25)⋊C9 |
| derived, Sylow | C31 ⋊ C9×C25 |
| Hall | C31⋊C25 ⋊ C9 |
| Hall | C31⋊C9 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3×C5 | (C31⋊C3)⋊C5 |
| commutator, hypocenter | C31 | C9×C25 |
| Fitting, socle | C3×C5×C31 | C3×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C5 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
3,5,31,3,5|a^3=d,b^5=e,c^a=c^25,c^b=c^16255 conjugacy classes — view the full character table.
| maximal subgroup of | (D31⋊C9)⋊C25, C2×(C31⋊C9)⋊C25, C22⋊((C31⋊C9)⋊C25) |
| maximal normal subgroup of | (D31⋊C9)⋊C25, C2×(C31⋊C9)⋊C25 |
| maximal quotient of | C2×(C31⋊C9)⋊C25, C22⋊((C31⋊C9)⋊C25) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6975, 2);