#11920746

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, hypercenter	C₂	#10593244
commutator, prime radical, cosocle	C₂×C₃×C₂²⋊A₄	C₂²
Frattini	C₂³	D₃×S₄
Fitting	C₂⁵×C₃	C₂×D₃
socle	C₂³×C₃	C₂×S₄
hypocenter	C₃×C₂²⋊A₄	Q₈
LCS	G ▷ C₂×C₃×C₂²⋊A₄ ▷ C₃×C₂²⋊A₄
UCS	C₁ ◁ C₂

371 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 371 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.

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

μ_t(G) = 72

Polycyclic presentation:

2^3,3^2,2^4|a^2=c,b^2=c,b^a=bc,e^a=e^2,f^a=fh,g^a=gi,d^b=d^2,f^b=fg,h^b=hi,f^d=g,g^d=fg,h^d=i,i^d=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 154757);