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#11866250

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

Splittings

C₉ ⋊ #3042

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₄×D₉
commutator, cosocle	C₂×C₄×C₉	C₂⁴
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂×C₉×AGL(1,ℤ/8)	C₂
socle	C₂²×C₃	C₂×D₃×D₄
prime radical	C₂×C₃×AGL(1,ℤ/8)	D₃
hypercenter	C₂×AGL(1,ℤ/8)	D₉
hypocenter	C₉	#3042
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

741 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 288

Polycyclic presentation:

2^7,3^2|a^2=g,b^2=e,f^2=g,h^3=i,b^a=be,c^a=cf,f^a=fg,h^a=h^2i^2,i^a=i^2,d^b=dg,h^b=h^2i^2,i^b=i^2,f^c=fg

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 100261);