Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C52 ⋊ M16 |
| Sylow | C52 ⋊ ΓL(1,𝔽25) |
| Sylow | C3 ⋊ #87769 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D5×D15 |
| commutator, socle | C2×C3×C52 | C2×C4 |
| Fitting, cosocle | C3×C4×C52 | C22 |
| prime radical | C2×C3⋊(C5⋊D5) | C4 |
| hypocenter | C3×C52 | M16 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C4 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,b^2=c,c^2=d,b^a=bd,e^a=e^2,f^a=f^4,g^b=g^4138 conjugacy classes — view the full character table.
| maximal subgroup of | #72229572, #72230510, D3×#87769, … |
| maximal normal subgroup of | #72229572, #72230510, D3×#87769, … |
| maximal quotient of | #72260094 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 339);