Finite Group DatabasebetaFinite Group Databasebeta| order | 750 |
| isoclinism | isoclinic class of #6953 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#6953 |
| Fitting, Hall | C3×H(3,𝔽5) ⋊ C2 |
| derived, Sylow | H(3,𝔽5) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C3×C5 | C5⋊D5 |
| commutator, cosocle, hypocenter | H(3,𝔽5) | C2×C3 |
| Frattini | C5 | C3×C5⋊D5 |
| Fitting | C3×H(3,𝔽5) | C2 |
| LCS | G ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C3×C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 75 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#92537, C3×#92539, C3⋊#92537, … |
| maximal normal subgroup of | C3×#92537, C3×#92539, C3⋊#92537, … |
| maximal quotient of | C3×#92525, C2×C3×#6953, ΓL(1,𝔽8)×#6953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(750, 13);