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.
| Fitting | C52×Q8 ⋊ C2 |
| Sylow | C52 ⋊ SD16 |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 200 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2,4,6)(3,8,7,5)(14,15,17,18,16);(2,5)(3,7)(6,8)(10,11)(12,13)(15,16)(17,18);(9,10,12,13,11)Polycyclic presentation:
2^4,5^2|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×#688, #11717057, #11717066, … |
| maximal normal subgroup of | D5×#688, #11717057, #11717066, … |
| maximal quotient of | #11716675, #11716676, #11716702, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 105);