C₅²×C₇×C₃⋊AGL(1,𝔽₇) #36348022

order	22050
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅²×C₇ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×C₇×C₃⋊AGL(1,𝔽₇)
unambiguous semidirect product	C₃⋊(C₅²×C₇×AGL(1,𝔽₇))
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₅²×D₃×C₇)
unambiguous semidirect product	D₂₁⋊(C₃×C₅²×C₇)
unambiguous semidirect product	(C₅×D₂₁)⋊(C₃×C₅×C₇)

	subgroup	G/H
center, hypercenter	C₅²×C₇	C₃⋊AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₃×C₅²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇²	C₂×C₃
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₅²×C₇

304 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.

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

μ_t(G) = 3150

2100 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 459);