D₃×C₁₇×C₅⋊AGL(1,𝔽₇) #36339385

order	21420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₁₇×C₅⋊AGL(1,𝔽₇)
unambiguous semidirect product	(C₅×D₃)⋊(C₁₇×AGL(1,𝔽₇))
unambiguous semidirect product	(D₃×ΓL(1,𝔽₈))⋊(D₅×C₁₇)
unambiguous semidirect product	(D₃×D₃₅)⋊(C₃×C₁₇)
unambiguous semidirect product	(D₃×C₁₇×D₃₅)⋊C₃

	subgroup	G/H
center, hypercenter	C₁₇	D₃×C₅⋊AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₃×C₅×C₇	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₇	C₂²×C₃
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₁₇

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

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

μ_t(G) = 1785

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 217);