#28383711

order	14272
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₂₂₃ ⋊ #446

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₂₃
commutator, socle, prime radical	C₂²×C₂₂₃	C₂²×C₄
Fitting	C₄×Q₈×C₂₂₃	C₂
cosocle	C₂×C₄×C₂₂₃	C₂³
hypercenter	C₄×Q₈	D₂₂₃
hypocenter	C₂₂₃	#446
LCS	G ▷ C₂²×C₂₂₃ ▷ C₂₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

94 conjugacy classes of subgroups.

μ_t(G) = 14272

Polycyclic presentation:

2^6,223|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^222,g^c=g^222

2248 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14272, 680);