AGL(1,𝔽₇)×#3773 #72217854

order	6048
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂³

Aliases

Hall	C₃²×ΓL(1,𝔽₈) ⋊ C₂×C₄⋊C₄
Sylow	C₇ ⋊ C₂×C₃×#3773

	subgroup	G/H
center, Frattini, hypercenter	C₂	AGL(1,𝔽₇)×GO⁺(4,𝔽₂)
commutator	C₇×C₃⋊D₃	C₂²×C₃×C₄
Fitting, socle	C₂×C₃²×C₇	C₂×C₃×D₄
prime radical	C₂×C₃⋊D₃×AGL(1,𝔽₇)	C₂²
cosocle	C₂×C₇×C₃⋊D₃	C₂³×C₃
hypocenter	C₃²×C₇	C₂×C₃×C₄⋊C₄
LCS	G ▷ C₇×C₃⋊D₃ ▷ C₃²×C₇
UCS	C₁ ◁ C₂

648 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

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

maximal subgroup of	C₄×AGL(1,𝔽₇)×GO⁺(4,𝔽₂)
maximal normal subgroup of	C₄×AGL(1,𝔽₇)×GO⁺(4,𝔽₂)

Past the SmallGroups library coverage — no SmallGroups id.