Finite Group DatabasebetaFinite Group Databasebeta| order | 750 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#3874 |
| Fitting, socle, Sylow | C53 ⋊ D3 |
| derived | C52⋊C3 ⋊ C2×C5 |
| Hall | C5×C52⋊C3 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #3874 |
| commutator, cosocle, hypocenter | C52⋊C3 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C53 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C5 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#3874⋊C2, #3874⋊D5, D5×#3874, … |
| maximal normal subgroup of | C5×#3874⋊C2, #3874⋊D5, D5×#3874, … |
| maximal quotient of | C5×#64470, C2×C5×#3874, C5×C5⋊#3874 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(750, 26);