Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #64480 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| derived, Hall | C52⋊C3 ⋊ C2×C8 |
| Sylow | C52 ⋊ C2×C3⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #64480 |
| commutator, hypocenter | C52⋊C3 | C2×C8 |
| Frattini | C2 | C2×#64480 |
| Fitting | C4×C52 | Dic3 |
| socle | C2×C52 | C2×Dic3 |
| prime radical | C2×(C5⋊D5)⋊C3 | C4 |
| cosocle | #1039⋊C3 | C22 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C4 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,b^2=d,c^2=d,e^a=e^2,f^a=f^3g^3,g^a=g^2,f^c=f^4,g^c=g^4,f^e=fg,g^e=f^2g^332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 492);