#41006849

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

Aliases

No aliases for this group.

	subgroup	G/H
center	C₃²	C₃×C₃²⋊(C₃₇⋊C₃)
commutator, prime radical, cosocle	C₃³×C₃₇	C₃³
Frattini	C₃³	C₃²×C₃₇⋊C₃
Fitting	C₃×C₉²×C₃₇	C₃
socle	C₃²×C₃₇	C₃×H(3,𝔽₃)
hypercenter	C₃×C₉²	C₃₇⋊C₃
hypocenter	C₃₇	#10624787
LCS	G ▷ C₃³×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃²×C₉ ◁ C₃×C₉²

238 conjugacy classes of subgroups.

μ_t(G) = 8991

Polycyclic presentation:

3^6,37|a^3=f,b^3=d,c^3=f^2,b^a=bd,c^a=ce,e^a=ef,g^a=g^10

3021 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 2620);