Finite Group DatabasebetaFinite Group Databasebeta| order | 750 |
| isoclinism | isoclinic class of C5⋊#3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#3874 |
| Fitting, socle, Sylow | C53 ⋊ D3 |
| derived, Hall | C5×C52⋊C3 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C52⋊C3 | C2 |
| Fitting, socle | C53 | D3 |
| LCS | G ▷ C5×C52⋊C3 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15 |
Polycyclic presentation:
2,3,5^3|b^a=b^2,c^a=c^4,e^a=d^4e^4,d^b=de^3,e^b=d^4e^335 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊D5, ((C5⋊D5)⋊C3)⋊D5, D5×#3874, … |
| maximal normal subgroup of | #3874⋊D5, ((C5⋊D5)⋊C3)⋊D5, D5×#3874, … |
| maximal quotient of | #13093798, C2×C5⋊#3874, C5×C5⋊#3874 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(750, 27);