C₅×D₇×C₃⋊AGL(1,𝔽₁₁) #37528440

order	23100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅² · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₅×D₇×C₃⋊AGL(1,𝔽₁₁)
unambiguous semidirect product	(C₃×D₇)⋊(C₅×AGL(1,𝔽₁₁))
unambiguous semidirect product	(D₇×C₁₁⋊C₅)⋊(C₅×D₃)
unambiguous semidirect product	(D₇×D₃₃)⋊C₅²
unambiguous semidirect product	(C₅×D₇×D₃₃)⋊C₅

	subgroup	G/H
center, hypercenter	C₅	D₇×C₃⋊AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₃×C₇×C₁₁	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₁	C₂²×C₅
LCS	G ▷ C₃×C₇×C₁₁
UCS	C₁ ◁ C₅

320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

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

μ_t(G) = 1155

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 251);