#11794595

order	1152
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

Sylow

C₃² ⋊ #2068

Subgroups

	subgroup	G/H
center	C₂³	C₂×#626
commutator, cosocle	C₂²×C₃²×C₄	C₂³
Frattini	C₂²×C₄	C₂×D₃²
Fitting	C₂×C₃²×C₄²	C₂²
socle, prime radical	C₂³×C₃²	C₂×D₄
hypercenter	C₂×C₄²	D₃²
hypocenter	C₃²	#2068
LCS	G ▷ C₂²×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

589 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 384

Polycyclic presentation:

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

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 28606);