D₇×#87832 #72243107

order	5600
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇×D₅⋊AGL(1,𝔽₅)
commutator, Fitting, socle	C₂×C₅²×C₇	C₂²×C₄
prime radical	C₂×D₇×C₅⋊D₅	C₂²
cosocle	C₂×C₇×C₅⋊D₅	C₂³
hypocenter	C₅²×C₇	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₅²×C₇ ▷ C₅²×C₇
UCS	C₁ ◁ C₂

476 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 78 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	D₇×#11717375, AGL(1,𝔽₇)×#87832
maximal normal subgroup of	D₇×#11717375, AGL(1,𝔽₇)×#87832

Past the SmallGroups library coverage — no SmallGroups id.