#11760743

order	1056
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²	C₂×D₃×D₁₁
commutator, socle, prime radical, cosocle	C₂²×C₃×C₁₁	C₂³
Fitting	C₂×C₃×C₄×C₁₁	C₂²
hypercenter	C₂×C₄	D₃×D₁₁
hypocenter	C₃×C₁₁	#125
LCS	G ▷ C₂²×C₃×C₁₁ ▷ C₃×C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄

112 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

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

μ_t(G) = 1056

Polycyclic presentation:

2^5,3,11|a^2=e,b^2=d,c^2=e,c^a=cde,g^a=g^10,c^b=cd,f^b=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1056, 280);