Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of #87809 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Sylow | C52 ⋊ Q16 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 400 |
A minimal faithful permutation representation — 3 generators on 26 points:
(1,3,5,11)(2,6,8,15)(4,13,14,10)(7,16,12,9)(22,23,25,26,24);(1,2,5,8)(3,9,11,16)(4,12,14,7)(6,13,15,10)(18,19)(20,21)(23,24)(25,26);(17,18,20,21,19)Polycyclic presentation:
2^4,5^2|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^4,f^a=f^4,c^b=cd67 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#689, #11717061, #11717064, … |
| maximal normal subgroup of | D5×#689, #11717061, #11717064, … |
| maximal quotient of | #11716674, #11716677, #11716702, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 106);