Finite Group DatabasebetaFinite Group Databasebeta| order | 10075 |
| automorphism | ? |
| homology | Abelianization (H1) = C13×C25 · Schur multiplier (H2) = C1 |
| direct product | C13×C31⋊C25 |
| unambiguous semidirect product | C31⋊(C13×C25) |
| unambiguous semidirect product | (C13×C31)⋊C25 |
| derived, Sylow | C31 ⋊ C13×C25 |
| Hall | C13×C31 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C13 | ΓL(1,𝔽32) |
| commutator, hypocenter | C31 | C13×C25 |
| Frattini | C5 | C13×ΓL(1,𝔽32) |
| Fitting, socle, prime radical | C5×C13×C31 | C5 |
| cosocle | C5×C31 | C5×C13 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C5×C13 | |
12 conjugacy classes of subgroups.
715 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C13×C31⋊C25, C13×D31⋊C25, D13×C31⋊C25, … |
| maximal normal subgroup of | C2×C13×C31⋊C25, C13×D31⋊C25, D13×C31⋊C25, … |
| maximal quotient of | C2×C13×C31⋊C25, C3×C13×C31⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10075, 2);