#31771657

order	17216
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₂₆₉ ⋊ #446

	subgroup	G/H
center, Frattini	C₂²	C₂²×#11761640
commutator, socle, prime radical	C₂²×C₂₆₉	C₂²×C₄
Fitting	C₄⋊C₄×C₂₆₉	C₄
cosocle	C₂×Dic₂₆₉	C₂³
hypercenter	C₄⋊C₄	#11761640
hypocenter	C₂₆₉	#446
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

94 conjugacy classes of subgroups.

μ_t(G) = 17216

Polycyclic presentation:

2^6,269|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^82,g^b=g^268,g^c=g^187,g^e=g^268

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17216, 1601);