ΓL(1,𝔽₈)×#3712 #72254137

order	3024
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

Hall	C₃²×ΓL(1,𝔽₈) ⋊ M₁₆
Sylow	C₇ ⋊ C₃×#3712

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃²×ΓL(1,𝔽₈)
commutator, socle	C₂×C₃²×C₇	C₂×C₃×C₄
Fitting, cosocle	C₃²×C₄×C₇	C₂²×C₃
prime radical	C₂×C₃⋊D₃×ΓL(1,𝔽₈)	C₄
hypocenter	C₃²×C₇	C₃×M₁₆
LCS	G ▷ C₂×C₃²×C₇ ▷ C₃²×C₇
UCS	C₁ ◁ C₄

236 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

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

μ_t(G) = 168

maximal subgroup of	ΓL(1,𝔽₈)×#63818, AGL(1,𝔽₇)×#3712, #72254166, …
maximal normal subgroup of	ΓL(1,𝔽₈)×#63818, AGL(1,𝔽₇)×#3712, #72254166, …

Past the SmallGroups library coverage — no SmallGroups id.