#11772363

order	1152
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₈	GO⁺(4,𝔽₂)
commutator	C₃⋊Dic₃	C₄×C₈
Fitting	C₂×C₃²×C₈	D₄
socle	C₂²×C₃²	C₂²⋊C₈
prime radical	C₂²×C₃⋊D₃	M₁₆
cosocle	C₂×C₈×C₃⋊D₃	C₂²
hypocenter	C₃²	#1379
LCS	G ▷ C₃⋊Dic₃ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₈

246 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

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

μ_t(G) = 192

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 6374);