Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | #41⋊(C52⋊C3) |
| Fitting, Hall | C52×#41 ⋊ C3 |
| Sylow | C52 ⋊ #41⋊C3 |
| Sylow | #41 ⋊ C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C22⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C52×Q8 | C2×C3 |
| Frattini | C2 | C2×C22⋊(C52⋊C3) |
| Fitting | C52×#41 | C3 |
| socle | C2×C52 | C2×A4 |
| LCS | G ▷ C52×Q8 | |
| UCS | C1 ◁ C4 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2,3,2^2,5^2,2|a^2=g,c^2=g,d^2=g,c^b=cd,d^b=c,e^b=e^3f^2,f^b=ef,d^c=dg94 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 884);