Finite Group DatabasebetaFinite Group Databasebeta| order | 8175 |
| isoclinism | isoclinic class of C109⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×C109⋊C3 |
| unambiguous semidirect product | C109⋊(C3×C25) |
| unambiguous semidirect product | (C25×C109)⋊C3 |
| Fitting, Hall | C25×C109 ⋊ C3 |
| derived, Sylow | C109 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C109⋊C3 |
| commutator, hypocenter | C109 | C3×C25 |
| Frattini | C5 | C5×C109⋊C3 |
| Fitting | C25×C109 | C3 |
| socle | C5×C109 | C3×C5 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C25 | |
12 conjugacy classes of subgroups.
975 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C25×C109⋊C3, C25×D109⋊C3, D25×C109⋊C3, … |
| maximal normal subgroup of | C2×C25×C109⋊C3, C25×D109⋊C3, D25×C109⋊C3, … |
| maximal quotient of | C2×C25×C109⋊C3, C25×#11758279, C3×C25×C109⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8175, 2);