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C₃×H(3,𝔽₃)⋊#4294 #28354669

order	13851
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉ · Schur multiplier (H₂) = C₃⁴

Aliases

C₃×H(3,𝔽₃)⋊#4294

Splittings

C₁₉ ⋊ C₃×H(3,𝔽₃)⋊C₉

Subgroups

	subgroup	G/H
center	C₃³	C₃²⋊(C₁₉⋊C₃)
commutator	C₃²×C₁₉	C₃²×C₉
Frattini	C₃³	C₃²×C₁₉⋊C₃
Fitting, prime radical	C₃²×C₁₉×H(3,𝔽₃)	C₃
socle	C₃³×C₁₉	H(3,𝔽₃)
cosocle	C₃³×C₁₉	C₃³
hypercenter	C₃²×H(3,𝔽₃)	C₁₉⋊C₃
hypocenter	C₁₉	C₃×H(3,𝔽₃)⋊C₉
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃³ ◁ C₃⁴ ◁ C₃²×H(3,𝔽₃)

680 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4617

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 2033);