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#49144402

order	36693
automorphism	?
homology	Abelianization (H₁) = C₉² · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

Splittings

C₁₅₁ ⋊ #6864

Subgroups

	subgroup	G/H
center, Frattini	C₃×C₉	C₃×C₁₅₁⋊C₃
commutator	C₃×C₁₅₁	C₉²
Fitting	C₃×C₂₇×C₁₅₁	C₃
socle, prime radical	C₃²×C₁₅₁	C₃×C₉
cosocle	C₃×C₉×C₁₅₁	C₃²
hypercenter	C₃×C₂₇	C₁₅₁⋊C₃
hypocenter	C₁₅₁	#6864
LCS	G ▷ C₃×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₃×C₉ ◁ C₃×C₂₇

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 36693

Polycyclic presentation:

3^5,151|a^3=c,b^3=d,c^3=e,b^a=be,f^b=f^32

Conjugacy classes & character table

4149 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36693, 90);