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#28354613

order	13851
automorphism	?
homology	Abelianization (H₁) = C₃×C₉² · Schur multiplier (H₂) = C₃×C₉

Aliases

No aliases for this group.

Splittings

C₁₉ ⋊ #10624681

Subgroups

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₁₉⋊C₃
commutator	C₃×C₁₉	C₃×C₉²
Fitting	C₃×C₁₉×C₂₇⋊C₃	C₃
socle	C₃²×C₁₉	C₃²×C₉
prime radical	C₃³×C₁₉	C₃×C₉
cosocle	C₃×C₉×C₁₉	C₃³
hypercenter	C₃×C₂₇⋊C₃	C₁₉⋊C₃
hypocenter	C₁₉	#10624681
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃×C₂₇⋊C₃

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4617

Polycyclic presentation:

3^6,19|a^3=d,b^3=e,d^3=f,g^a=g^11,c^b=cf,g^b=g^7

Conjugacy classes & character table

891 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 1977);