C₄⋊#1042 #87851

order	400
isoclinism	isoclinic class of #87849
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

Fitting	C₄×C₅² ⋊ C₄
Sylow	C₅² ⋊ C₄⋊C₄

55 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 14 points:

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

Polycyclic presentation:

2^4,5^2|a^2=c,b^2=d,b^a=bd,e^a=e^4,f^a=f^3,f^c=f^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 145);