Finite Group DatabasebetaFinite Group Databasebeta| order | 1125 |
| isoclinism | isoclinic class of H(3,𝔽5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×H(3,𝔽5)⋊C3 |
| unambiguous semidirect product | H(3,𝔽5)⋊C32 |
| unambiguous semidirect product | (C3×H(3,𝔽5))⋊C3 |
| Fitting | C3×H(3,𝔽5) ⋊ C3 |
| derived, Sylow | H(3,𝔽5) ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C3×C5 | C52⋊C3 |
| commutator, cosocle, hypocenter | H(3,𝔽5) | C32 |
| Frattini | C5 | C3×C52⋊C3 |
| Fitting | C3×H(3,𝔽5) | C3 |
| LCS | G ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C3×C5 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 225 |
69 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1125, 7);