Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #13103248 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | C24⋊C25 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C24⋊C25 | C4 |
| Frattini | C5 | #66297 |
| Fitting, socle | C24×C5 | AGL(1,𝔽5) |
| prime radical, cosocle | (C24⋊C25)⋊C2 | C2 |
| LCS | G ▷ C24⋊C25 | |
| UCS | C1 | |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 50 |
Polycyclic presentation:
2^2,5^2,2^4|a^2=b,c^5=d,c^a=c^2d,d^a=d^2,e^a=eg,f^a=fh,g^a=fgh,c^b=c^4d^4,d^b=d^4,e^b=efh,g^b=gh,e^c=efg,f^c=ef,g^c=gh,h^c=eg19 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5600);