#11798026

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂×C₃

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#157
commutator, socle, prime radical	C₂²×C₃²	C₂²×C₈
Fitting	C₃²×C₄⋊C₈	C₄
cosocle	C₂×C₃⋊(C₃⋊C₈)	C₂³
hypercenter	C₄⋊C₈	#157
hypocenter	C₃²	#2183
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

228 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

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

μ_t(G) = 384

Polycyclic presentation:

2^7,3^2|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^2i^2,i^a=h^2i,h^b=h^2,i^b=i^2,h^c=hi,i^c=hi^2,h^e=h^2,i^e=i^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 32037);