#26132680

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₄₇
commutator, socle, prime radical	C₂³×C₄₇	C₂²×C₈
Fitting	C₄₇×#1726	C₂
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#1726	D₄₇
hypocenter	C₄₇	#12895
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₈ ◁ #1726

298 conjugacy classes of subgroups.

Polycyclic presentation:

2^8,47|a^2=f,b^2=de,c^2=d,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^46,c^b=ch

1928 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 85970);