C₂₉×D₁₅⋊AGL(1,𝔽₇) #49141490

order	36540
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂₉×D₁₅⋊AGL(1,𝔽₇)
unambiguous semidirect product	D₁₅⋊(C₂₉×AGL(1,𝔽₇))
unambiguous semidirect product	(C₃⋊AGL(1,𝔽₇))⋊(D₅×C₂₉)
unambiguous semidirect product	(C₅⋊AGL(1,𝔽₇))⋊(D₃×C₂₉)
unambiguous semidirect product	(D₁₅⋊D₇)⋊(C₃×C₂₉)
unambiguous semidirect product	(C₂₉×D₁₅⋊D₇)⋊C₃

	subgroup	G/H
center, hypercenter	C₂₉	D₁₅⋊AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₃×C₅×C₇	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₂²×C₃
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₂₉

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) = 3045

1305 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 332);