Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C25 ⋊ #41 |
| Sylow | C25 ⋊ #239 |
| Sylow | C3 ⋊ #87746 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D3×D25 |
| commutator, cosocle | C2×C3×C25 | C23 |
| Frattini | C2×C5 | C2×D3×D5 |
| Fitting | C3×C4×C25 | C22 |
| socle | C2×C3×C5 | C22×D5 |
| hypercenter | C4 | D3×D25 |
| hypocenter | C3×C25 | #41 |
| LCS | G ▷ C2×C3×C25 ▷ C3×C25 | |
| UCS | C1 ◁ C2 ◁ C4 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
Polycyclic presentation:
2^4,3,5^2|a^2=d,c^2=d,f^5=g,c^a=cd,f^a=f^4g^4,g^a=g^4,c^b=cd,e^b=e^2123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 126);