C₃×AGL(1,𝔽₇)×#997 #72244667

order	12096
automorphism	?
homology	Abelianization (H₁) = C₂×C₃³ · Schur multiplier (H₂) = C₂³×C₃³

Aliases

	subgroup	G/H
center, hypercenter	C₂×C₃	AGL(1,𝔽₇)×C₂²⋊A₄
commutator, cosocle, hypocenter	C₇×H(5,𝔽₂)	C₂×C₃³
Frattini	C₂	C₃×AGL(1,𝔽₇)×C₂²⋊A₄
Fitting	C₃×C₇×H(5,𝔽₂)	C₂×C₃²
socle	C₂×C₃×C₇	C₂×C₃×C₂²⋊A₄
LCS	G ▷ C₇×H(5,𝔽₂)
UCS	C₁ ◁ C₂×C₃

3148 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 3148 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.

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

μ_t(G) = 168

Past the SmallGroups library coverage — no SmallGroups id.