#11770760

order	1152
isoclinism	isoclinic class of AΓL(1,𝔽₉)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	AΓL(1,𝔽₉)
commutator	#157	C₄×C₈
Fitting	C₂×C₃²×C₄	SD₁₆
socle	C₂²×C₃²	#106
prime radical	C₂²×C₃⋊D₃	C₄⋊C₄
cosocle	C₂×C₄×#157	C₂²
hypocenter	C₃²	#1277
LCS	G ▷ #157 ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₂×C₄

218 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

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

μ_t(G) = 144

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,h^a=hi,i^a=i^2,h^b=h^2i,i^b=h,h^c=h^2i^2,i^c=h^2i,h^e=h^2i^2,i^e=h^2i,h^f=h^2,i^f=i^2

maximal subgroup of	#72244965, #72252960, #72252964
maximal normal subgroup of	#72244965, #72252960, #72252964

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4771);