Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of #87735 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#1035 |
| unambiguous semidirect product | (C2×#1035)⋊C2 |
| Fitting | C22×C25 ⋊ C4 |
| Sylow | C25 ⋊ C22⋊C4 |
51 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 100 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,7,12,10,5,3,19,17,15,13,8,25,24,16,22,20,21,6,11,14,9,2,4,23,18)(27,29);(2,4,5,10)(3,8,9,20)(6,14,15,19)(7,17,18,11)(12,22,23,25)(13,16,21,24)(26,27)(28,29)Polycyclic presentation:
2^4,5^2|a^2=c,e^5=f,b^a=bd,e^a=e^2f,f^a=f^2,e^c=e^4f^4,f^c=f^434 conjugacy classes — view the full character table.
| maximal subgroup of | #11716421, #11716429, #11716549, … |
| maximal normal subgroup of | #11716421, #11716429, #11716549, … |
| maximal quotient of | #11716418, #11716420, #11716421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 34);