#46812794

order	34432
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₂₆₉ ⋊ #2183

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₂₆₉
commutator, socle, prime radical	C₂²×C₂₆₉	C₂²×C₈
Fitting	C₈×Q₈×C₂₆₉	C₂
cosocle	C₂×C₈×C₂₆₉	C₂³
hypercenter	C₈×Q₈	D₂₆₉
hypocenter	C₂₆₉	#2183
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

126 conjugacy classes of subgroups.

μ_t(G) = 34432

Polycyclic presentation:

2^7,269|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^268,h^c=h^268

5416 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 6419);