#14762118

order	2816
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₁
commutator, socle, prime radical	C₂³×C₁₁	C₂³×C₄
Fitting	C₁₁×#1832	C₂
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	#1832	D₁₁
hypocenter	C₁₁	#21677
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ #1832

618 conjugacy classes of subgroups; only the 231 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 231 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 2816

Polycyclic presentation:

2^8,11|a^2=g,b^2=f,c^2=e,d^2=eg,g^2=h,b^a=be,c^a=cf,d^a=dh,c^b=ch,i^d=i^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 177913);