Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | 2−1+4⋊C25 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C24⋊C25)⋊C2 |
| commutator, cosocle, hypocenter | 2−1+4⋊C25 | C2 |
| Frattini, socle | C2×C5 | (C24⋊C5)⋊C2 |
| Fitting | C5×2−1+4 | D5 |
| LCS | G ▷ 2−1+4⋊C25 | |
| UCS | C1 ◁ C2 | |
97 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2,5^2,2^5|b^5=c,d^2=h,e^2=h,f^2=h,b^a=b^4c^4,c^a=c^4,d^a=degh,e^a=eh,f^a=fgh,d^b=e,e^b=deg,f^b=dfh,g^b=defgh,f^d=fh,g^d=gh,f^e=fh40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2008);