#11787531

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

Splittings

Fitting	C₉×#390 ⋊ C₂
Sylow	C₉ ⋊ #1879

Subgroups

	subgroup	G/H
center	C₂³	C₂×#611
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#390	C₂
socle	C₂³×C₃	C₂×#67
prime radical	C₂²×#3673	C₂
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	#390	D₉
hypocenter	C₉	#1879
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

657 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 576

Polycyclic presentation:

2^7,3^2|a^2=f,b^2=dfg,d^2=g,e^2=g,f^2=g,h^3=i,b^a=bd,c^a=ce,h^a=h^2i^2,i^a=i^2,d^b=dg,e^b=eg,f^b=fg,h^b=h^2i^2,i^b=i^2,d^c=dg,e^c=eg,f^c=fg,h^c=h^2i^2,i^c=i^2

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 21542);