Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C5 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | C5⋊D5 |
| commutator, hypocenter | C52 | C32 |
| Fitting, cosocle | C52×C16 | C2 |
| socle, prime radical | C2×C52 | C16 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C16 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^5,5^2|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^4,g^a=g^4224 conjugacy classes — view the full character table.
| maximal subgroup of | #13099234, #13099235, D5×#3926, … |
| maximal normal subgroup of | #13099234, #13099235, D5×#3926, … |
| maximal quotient of | #13098661, C2×#11716541 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 200);