#28411608

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	C₂×C₄	C₂²×D₂₂₉
commutator, socle, prime radical	C₂²×C₂₂₉	C₂²×C₄
Fitting	C₄⋊C₈×C₂₂₉	C₂
cosocle	C₂×C₄×C₂₂₉	C₂³
hypercenter	C₄⋊C₈	D₂₂₉
hypocenter	C₂₂₉	#446
LCS	G ▷ C₂²×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

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^c=g^228

2308 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 676);