AGL(1,ℤ/8)×#509 #72342612

order	2048
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹³

Aliases

	subgroup	G/H
center, socle	C₂²	C₂²×D₄×D₈
commutator, Frattini, cosocle	C₄×C₈	C₂⁶
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×C₈×AGL(1,ℤ/8) ◁ G
LECS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

At least 9737 conjugacy classes of subgroups; only the 3954 normal subgroups are shown.

maximal subgroup of	AGL(1,ℤ/8)×AGL(1,ℤ/16)
maximal normal subgroup of	AGL(1,ℤ/8)×AGL(1,ℤ/16)

Past the SmallGroups library coverage — no SmallGroups id.