Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D3×D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C3×C25 ⋊ C2×C8 |
| Sylow | C25 ⋊ D3×C8 |
| Sylow | C3 ⋊ C8×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D3×D25 |
| commutator, hypocenter | C3×C25 | C2×C8 |
| Frattini | C4×C5 | D3×D5 |
| Fitting, cosocle | C3×C4×C25 | C22 |
| socle | C2×C3×C5 | C4×D5 |
| prime radical | C2×D75 | C4 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C4 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,b^2=c,c^2=d,f^5=g,f^a=f^4g^4,g^a=g^4,e^b=e^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 8);