C₅×(C₂×AGL(1,𝔽₅))⋊C₈ #13100082

order	1600
isoclinism	isoclinic class of #700
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₈ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₅×(C₂×AGL(1,𝔽₅))⋊C₈
unambiguous semidirect product	(C₂×AGL(1,𝔽₅))⋊(C₅×C₈)

Fitting	C₂×C₅²×C₈ ⋊ C₄
Sylow	C₅² ⋊ #336

247 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 247 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.

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

μ_t(G) = 320

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 2434);