Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C3×C52 ⋊ C2×C8 |
| Sylow | C52 ⋊ D3×C8 |
| Sylow | C3 ⋊ #87827 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×D15 |
| commutator, hypocenter | C3×C52 | C2×C8 |
| Fitting, socle | C2×C3×C52 | C2×C4 |
| prime radical | C2×C3⋊(C5⋊D5) | C4 |
| cosocle | C3×C5×Dic5 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5^2|a^2=d,b^2=c,c^2=d,e^a=e^2,g^a=g^4,f^b=f^2,f^c=f^490 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#87827, #72231061, #72231067, … |
| maximal normal subgroup of | D3×#87827, #72231061, #72231067 |
| maximal quotient of | #72231168 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 578);