C₅×D₅₁⋊AGL(1,𝔽₇) #36339362

order	21420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₅₁⋊AGL(1,𝔽₇)
unambiguous semidirect product	D₅₁⋊(C₅×AGL(1,𝔽₇))
unambiguous semidirect product	(C₃⋊AGL(1,𝔽₇))⋊(C₅×D₁₇)
unambiguous semidirect product	(C₁₇⋊AGL(1,𝔽₇))⋊(C₅×D₃)
unambiguous semidirect product	(D₂₁⋊D₁₇)⋊(C₃×C₅)
unambiguous semidirect product	(C₅×D₂₁⋊D₁₇)⋊C₃

	subgroup	G/H
center, hypercenter	C₅	D₅₁⋊AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₃×C₇×C₁₇	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₇	C₂²×C₃
LCS	G ▷ C₃×C₇×C₁₇
UCS	C₁ ◁ C₅

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

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

μ_t(G) = 1785

585 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 194);