Finite Group DatabasebetaFinite Group Databasebeta| order | 975 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×C13⋊C3 |
| unambiguous semidirect product | C13⋊(C3×C52) |
| unambiguous semidirect product | (C5×C13)⋊(C3×C5) |
| Fitting, socle, Hall | C52×C13 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 325 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | C52×D13⋊C3, C5×D5×C13⋊C3, C5×C5⋊(D13⋊C3), … |
| maximal normal subgroup of | C52×D13⋊C3, C5×D5×C13⋊C3, C5×C5⋊(D13⋊C3), … |
| maximal quotient of | C2×C52×C13⋊C3, C52×C13⋊C9, C3×C52×C13⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(975, 3);