Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of #6045 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C2×C4×C52 ⋊ C2 |
| Sylow | C52 ⋊ C22⋊C4 |
136 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 200 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2,3,4)(6,8)(14,15,17,18,16);(5,6)(7,8)(10,11)(12,13)(15,16)(17,18);(9,10,12,13,11)Polycyclic presentation:
2^4,5^2|b^2=c,b^a=bd,e^a=e^4,f^a=f^4106 conjugacy classes — view the full character table.
| maximal subgroup of | #11716954, #11716966, #11716968, … |
| maximal normal subgroup of | #11716954, #11716966, #11716968, … |
| maximal quotient of | #11716672, #11716673, #11716676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 102);