Finite Group DatabasebetaFinite Group Databasebeta| order | 750 |
| isoclinism | isoclinic class of #10625285 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | H(3,𝔽5) ⋊ D3 |
| derived, Hall | H(3,𝔽5)⋊C3 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | H(3,𝔽5)⋊C3 | C2 |
| Frattini, socle | C5 | #3874 |
| Fitting | H(3,𝔽5) | D3 |
| LCS | G ▷ H(3,𝔽5)⋊C3 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 75 |
Polycyclic presentation:
2,3,5^3|b^a=b^2,c^a=c^2de^4,d^a=c^2d^3,e^a=e^4,c^b=c^2d^4,d^b=c^2d^2e^4,d^c=de19 conjugacy classes — view the full character table.
| maximal subgroup of | #10625285⋊C2, C2×#10625285 |
| maximal normal subgroup of | #10625285⋊C2, C2×#10625285 |
| maximal quotient of | #13093712, C2×#10625285 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(750, 5);