Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #11925747 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C3×C52 ⋊ M16 |
| Sylow | C52 ⋊ #208 |
| Sylow | C3 ⋊ #6053⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator | C3×C5⋊D5 | C2×C4 |
| Fitting, socle, hypocenter | C3×C52 | M16 |
| prime radical | C3×D52 | C4 |
| cosocle | C3×#1043 | C22 |
| LCS | G ▷ C3×C5⋊D5 ▷ C3×C52 | |
| UCS | C1 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,c^2=d,b^a=bd,e^a=e^2,f^a=f^3g^3,g^a=fg^2,f^b=f^4g,f^c=f^2,g^c=g^2,f^d=f^4,g^d=g^427 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6053⋊C2, #72276832 |
| maximal normal subgroup of | D3×#6053⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 957);