#11770757

order	1152
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂²×C₄	GO⁺(4,𝔽₂)
commutator	C₃⋊Dic₃	C₄×C₈
Fitting	C₂²×C₃²×C₄	D₄
socle, prime radical	C₂³×C₃²	C₄⋊C₄
cosocle	C₂×C₄×C₃⋊Dic₃	C₂²
hypocenter	C₃²	#1277
LCS	G ▷ C₃⋊Dic₃ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₄

318 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 87 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=d,b^2=e,c^2=f,d^2=g,e^2=f,b^a=bc,c^a=cf,e^a=ef,i^a=hi^2,h^b=hi,i^b=hi^2,h^c=h^2,i^c=i^2,h^e=h^2,i^e=i^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4768);