ΓL(1,𝔽₈)×#87830 #72243120

order	8400
automorphism	?
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₄

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	ΓL(1,𝔽₈)×D₅⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅²×C₇	C₃×C₄²
Fitting, socle	C₂×C₅²×C₇	C₂×C₃×C₄
prime radical	C₂×ΓL(1,𝔽₈)×C₅⋊D₅	C₂²
cosocle	C₂×C₇×C₅⋊D₅	C₂²×C₃
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₂

304 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

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

μ_t(G) = 140

maximal subgroup of	AGL(1,𝔽₇)×#87830, ΓL(1,𝔽₈)×#11717375, #72243191
maximal normal subgroup of	AGL(1,𝔽₇)×#87830, ΓL(1,𝔽₈)×#11717375, #72243191

Past the SmallGroups library coverage — no SmallGroups id.