Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | #87756⋊C3 |
| derived, Sylow | C52 ⋊ C3×C16 |
| Hall | #87756 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | (C5⋊D5)⋊C3 |
| commutator, hypocenter | C52 | C3×C16 |
| Fitting, cosocle | C52×C8 | C2×C3 |
| socle | C2×C52 | C3×C8 |
| prime radical | C2×C52⋊C3 | C8 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C8 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2,3,2^3,5^2|a^2=c,c^2=d,d^2=e,f^a=f^4,g^a=g^4,f^b=fg,g^b=f^2g^380 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 184);