C₇×D₇×C₃⋊AGL(1,𝔽₁₁) #44568595

order	32340
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×D₇×C₃⋊AGL(1,𝔽₁₁)
unambiguous semidirect product	(C₃×D₇)⋊(C₇×AGL(1,𝔽₁₁))
unambiguous semidirect product	(D₇×C₁₁⋊C₅)⋊(D₃×C₇)
unambiguous semidirect product	(D₇×D₃₃)⋊(C₅×C₇)
unambiguous semidirect product	(C₇×D₇×D₃₃)⋊C₅

	subgroup	G/H
center, hypercenter	C₇	D₇×C₃⋊AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₃×C₇×C₁₁	C₂²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₁	C₂²×C₅
LCS	G ▷ C₃×C₇×C₁₁
UCS	C₁ ◁ C₇

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

normal subgroups only

This group has 208 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) = 462

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 297);