C₂×D₄×AGL(1,𝔽₅) #66257

order	320
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product	C₂×D₄×AGL(1,𝔽₅)
unambiguous semidirect product	D₅⋊(C₄×D₄)

Fitting	C₂×C₅×D₄ ⋊ C₄
Sylow	C₅ ⋊ C₂×C₄×D₄

426 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 4 generators on 11 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1595);