Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C52 ⋊ D8 |
| Sylow | C52 ⋊ D24 |
| Sylow | C3 ⋊ #87837 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #10597189 |
| commutator, cosocle | C3×#1039 | C22 |
| Fitting, socle | C2×C3×C52 | D4 |
| hypocenter | C3×C52 | D8 |
| LCS | G ▷ C3×#1039 ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5^2|b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^4,g^a=f^2g,f^b=f^3g^3,g^b=g^2,f^c=f^4,g^c=g^445 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 609);