#46812469

order	34432
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₂₆₉ ⋊ #2104

	subgroup	G/H
center	C₂	C₂₆₉⋊#401
commutator, prime radical, cosocle	C₂⁴×C₂₆₉	C₂³
Frattini	C₂⁴	C₂²×D₂₆₉
Fitting	#342×C₂₆₉	C₂
socle	C₂×C₂₆₉	#401
hypercenter	#342	D₂₆₉
hypocenter	C₂₆₉	#2104
LCS	G ▷ C₂⁴×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #342

178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.

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

μ_t(G) = 4304

Polycyclic presentation:

2^7,269|a^2=def,b^2=de,c^2=d,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,f^b=fg,e^c=eg,h^c=h^268

2971 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 6094);