Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of D5⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C42 |
| Fitting, socle | C2×C52 | C2×C4 |
| prime radical, cosocle | C2×C5⋊D5 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2 | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 20 |
A minimal faithful permutation representation — 2 generators on 14 points:
(1,2)(4,5)(6,7,10,8,9)(11,12,13,14);(2,3,4,5)(7,8,9,10)Polycyclic presentation:
2^4,5^2|a^2=c,b^2=d,e^a=e^3,f^a=f^3,e^b=e^4,e^c=e^4,f^c=f^428 conjugacy classes — view the full character table.
| maximal subgroup of | #11717300, #11717302, #6053⋊C4, … |
| maximal normal subgroup of | #11717300, #11717302, #6053⋊C4, … |
| maximal quotient of | #11716761, #11716762, #11716763, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 124);