C₁₆₉⋊C₁₆₉ #43270030

order	28561
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₁₃×C₁₆₉ · Schur multiplier (H₂) = C₁₃

Aliases

C₁₆₉⋊C₁₆₉

	subgroup	G/H
center, Frattini, socle, prime radical, cosocle	C₁₃²	C₁₃²
commutator	C₁₃	C₁₃×C₁₆₉
LCS	G ▷ C₁₃ ▷ C₁
UCS	C₁ ◁ C₁₃² ◁ G
LECS	G ▷ C₁₃² ▷ C₁

57 conjugacy classes of subgroups.

μ_t(G) = 28561

Polycyclic presentation:

13^4|a^13=d,b^13=c,b^a=bc

2353 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28561, 4);