#11857092

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²	C₂²×GO⁺(4,𝔽₂)
commutator, prime radical, cosocle	C₂²×C₃⋊D₃	C₂⁴
Fitting	C₃²×C₄²	D₄
socle	C₂²×C₃²	C₂²×D₄
hypercenter	C₄²	GO⁺(4,𝔽₂)
hypocenter	C₃²	#2868
LCS	G ▷ C₂²×C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₄²

938 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 195 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=e,b^2=e,c^2=f,d^2=g,b^a=be,c^a=cf,d^a=dg,i^a=hi^2,h^d=hi,i^d=hi^2,h^g=h^2,i^g=i^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 91103);