Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊(C5⋊(#41⋊C3)) |
| Hall | #87904 ⋊ C3 |
| Sylow | C52 ⋊ #41⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4×C5⋊D5 |
| commutator, Fitting, cosocle, hypocenter | C52×Q8 | C2×C3 |
| socle | C2×C52 | C2×A4 |
| LCS | G ▷ C52×Q8 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2,3,2^2,5^2,2|a^2=g,c^2=g,d^2=g,e^a=e^4,f^a=f^4,c^b=d,d^b=cd,d^c=dg98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 696);