Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of C42⋊(C52⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C4×C5 |
| unambiguous semidirect product | C42⋊(C52⋊C3) |
| unambiguous semidirect product | C52⋊(C42⋊C3) |
| Fitting, derived, Hall | C42×C52 ⋊ C3 |
| Sylow | C52 ⋊ C42⋊C3 |
| Sylow | C42 ⋊ C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C42×C52 | C3 |
| Frattini | C22 | C22⋊(C52⋊C3) |
| socle | C22×C52 | A4 |
| LCS | G ▷ C42×C52 | |
| UCS | C1 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
3,2^2,5^2,2^2|b^2=g,c^2=fg,b^a=c,c^a=bcf,d^a=de^3,e^a=d^4e^3,f^a=g,g^a=fg136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 384);