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#13258240

order	1792
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

C₇ ⋊ #10575

Subgroups

	subgroup	G/H
center	C₂³	#6516
commutator, cosocle	C₂×C₄²×C₇	C₂³
Frattini	C₂×C₄²	C₂²×D₇
Fitting	C₇×#2551	C₂
socle, prime radical	C₂³×C₇	#120
hypercenter	#2551	D₇
hypocenter	C₇	#10575
LCS	G ▷ C₂×C₄²×C₇ ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2551

478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1792

Polycyclic presentation:

2^8,7|a^2=d,b^2=d,c^2=dh,e^2=g,f^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fh,c^b=cf,e^b=eh,f^b=fh,e^c=eg,f^c=fh,i^c=i^6

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 74012);