Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of (C24⋊C25)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| derived | C24⋊C25 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C24⋊C25)⋊C2 |
| commutator, hypocenter | C24⋊C25 | C4 |
| Frattini | C2×C5 | (C24⋊C5)⋊C2 |
| Fitting, socle, prime radical | C25×C5 | D5 |
| cosocle | C2×C24⋊C25 | C2 |
| LCS | G ▷ C24⋊C25 | |
| UCS | C1 ◁ C2 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
Polycyclic presentation:
2^2,5^2,2^4|a^2=b,c^5=d,c^a=c^4d^4,d^a=d^4,e^a=efh,g^a=gh,e^c=f,f^c=efh,g^c=eg,h^c=efgh52 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2009);