#41005322

order	26973
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃²

Aliases

No aliases for this group.

	subgroup	G/H
center	C₃²	H(3,𝔽₃)×C₃₇⋊C₃
commutator, prime radical, cosocle	C₃³×C₃₇	C₃³
Frattini	C₃³	C₃²×C₃₇⋊C₃
Fitting	C₃₇×#6861	C₃
socle	C₃²×C₃₇	C₃×H(3,𝔽₃)
hypercenter	#6861	C₃₇⋊C₃
hypocenter	C₃₇	#10624588
LCS	G ▷ C₃³×C₃₇ ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ #6861

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

normal subgroups only

This group has 202 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) = 8991

Polycyclic presentation:

3^6,37|a^3=f,b^3=f,c^3=e,b^a=bd,d^a=de,g^a=g^10,d^b=df,g^b=g^10,g^c=g^26

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 1093);