Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C5 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | C5⋊D5 |
| commutator, hypocenter | C52 | C16 |
| Fitting, cosocle | C52×C8 | C2 |
| socle, prime radical | C2×C52 | C8 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C8 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 400 |
A minimal faithful permutation representation — 3 generators on 26 points:
(1,2,3,6,4,7,9,12,5,8,10,13,11,14,15,16)(18,19)(20,21)(23,24)(25,26);(22,23,25,26,24);(17,18,20,21,19)Polycyclic presentation:
2^4,5^2|a^2=b,b^2=c,c^2=d,e^a=e^4,f^a=f^4112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 50);