#28412531

order	14656
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₂₂₉ ⋊ #446

	subgroup	G/H
center, Frattini	C₂²	C₂²×#11745021
commutator, socle, prime radical	C₂²×C₂₂₉	C₂²×C₄
Fitting	C₄⋊C₄×C₂₂₉	C₄
cosocle	C₂×Dic₂₂₉	C₂³
hypercenter	C₄⋊C₄	#11745021
hypocenter	C₂₂₉	#446
LCS	G ▷ C₂²×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

94 conjugacy classes of subgroups.

μ_t(G) = 14656

Polycyclic presentation:

2^6,229|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^122,g^c=g^122,g^e=g^228

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 1599);