C₁₇×D₁₅⋊AGL(1,𝔽₇) #36339389

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

Aliases

direct product	C₁₇×D₁₅⋊AGL(1,𝔽₇)
unambiguous semidirect product	D₁₅⋊(C₁₇×AGL(1,𝔽₇))
unambiguous semidirect product	(C₃⋊AGL(1,𝔽₇))⋊(D₅×C₁₇)
unambiguous semidirect product	(C₅⋊AGL(1,𝔽₇))⋊(D₃×C₁₇)
unambiguous semidirect product	(D₁₅⋊D₇)⋊(C₃×C₁₇)
unambiguous semidirect product	(C₁₇×D₁₅⋊D₇)⋊C₃

	subgroup	G/H
center, hypercenter	C₁₇	D₁₅⋊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 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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 221);