AGL(1,𝔽₅)×#13049813 #72269712

order	25920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator	C₅×C₃⋊(C₃⋊(C₃⋊D₃))	C₂³×C₄
Fitting, socle, hypocenter	C₃⁴×C₅	C₂×C₄×D₄
prime radical	D₅×#13049813	C₂
cosocle	D₅×C₃⋊(C₃⋊(C₃⋊D₃))	C₂⁴
LCS	G ▷ C₅×C₃⋊(C₃⋊(C₃⋊D₃)) ▷ C₃⁴×C₅
UCS	C₁

6136 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 6136 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.

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

μ_t(G) = 60

Past the SmallGroups library coverage — no SmallGroups id.