Finite Group DatabasebetaFinite Group Databasebeta| order | 750 |
| isoclinism | isoclinic class of C5⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C53 |
| direct product | C3×C5⋊(C5⋊D5) |
| unambiguous semidirect product | C5⋊(C3×C5⋊D5) |
| Fitting, socle, Hall | C3×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊(C5⋊D5) |
| commutator, cosocle, hypocenter | C53 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C53 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C3 | |
256 conjugacy classes of subgroups.
| transitive degree | μt(G) = 375 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#92562, C3×#92563, C3⋊#92562, … |
| maximal normal subgroup of | C3×#92562, C3×#92563, C3⋊#92562, … |
| maximal quotient of | C3×#92553, C2×C3×C5⋊(C5⋊D5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(750, 34);