#41005267

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

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₃₇⋊C₃
commutator, socle, prime radical, cosocle	C₃³×C₃₇	C₃³
Fitting	C₃×C₃₇×C₉⋊C₉	C₃
hypercenter	C₃×C₉⋊C₉	C₃₇⋊C₃
hypocenter	C₃₇	#10624577
LCS	G ▷ C₃³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃³ ◁ C₃×C₉⋊C₉

296 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

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

μ_t(G) = 26973

Polycyclic presentation:

3^6,37|a^3=def,b^3=de^2,c^3=d,b^a=bd,c^a=ce,g^a=g^26,c^b=cf,g^c=g^26

1293 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 1038);