C₂²×C₂²⋊AGL(1,𝔽₅) #66269

order	320
isoclinism	isoclinic class of #700
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product	C₂²×C₂²⋊AGL(1,𝔽₅)
unambiguous semidirect product	D₅⋊(C₂×C₂²⋊C₄)
unambiguous semidirect product	(C₂×AGL(1,𝔽₅))⋊C₂³

Fitting	C₂⁴×C₅ ⋊ C₄
Sylow	C₅ ⋊ C₂²×C₂²⋊C₄

674 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 4 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1607);