C₂²×C₅×C₂²⋊AGL(1,𝔽₅) #13107736

order	1600
isoclinism	isoclinic class of #700
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product	C₂²×C₅×C₂²⋊AGL(1,𝔽₅)
unambiguous semidirect product	D₅⋊(C₂×C₅×C₂²⋊C₄)
unambiguous semidirect product	(C₂×AGL(1,𝔽₅))⋊(C₂³×C₅)

Fitting	C₂⁴×C₅² ⋊ C₄
Sylow	C₅² ⋊ C₂²×C₂²⋊C₄

1415 conjugacy classes of subgroups; only the 392 normal subgroups are shown.

normal subgroups only

This group has 1415 conjugacy classes of subgroups — too many to draw. Only its 392 normal subgroups are shown.

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

μ_t(G) = 160

280 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 10088);