Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C52⋊C3 ⋊ C16 |
| Sylow | C52 ⋊ C3⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #3874 |
| commutator, hypocenter | C52⋊C3 | C16 |
| Fitting | C52×C8 | D3 |
| socle | C2×C52 | C3⋊C8 |
| prime radical | C2×C52⋊C3 | C8 |
| cosocle | C8×C52⋊C3 | C2 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C8 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^4,3,5^2|a^2=b,b^2=c,c^2=d,e^a=e^2,f^a=f^2g^4,g^a=f^3g^3,f^e=f^2g^4,g^e=f^2g^2104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 183);