C₂²⋊(C₅⋊D₅) #6049

order	200
isoclinism	isoclinic class of #6045
automorphism	Aut(G) = C₂²×AGL(2,𝔽₅) (order 48000) · Inn(G) = C₂×C₅⋊D₅ · Out(G) = GL(2,𝔽₅)
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂²⋊(C₅⋊D₅)

Fitting	C₂²×C₅² ⋊ C₂
Sylow	C₅² ⋊ D₄

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 100

A minimal faithful permutation representation — 3 generators on 14 points:

(2,4)(10,11,13,14,12);(1,2)(3,4)(6,7)(8,9)(11,12)(13,14);(5,6,8,9,7)

Polycyclic presentation:

2^3,5^2|b^a=bc,d^a=d^4,e^a=e^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(200, 36);