#26107431

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

C₄₇ ⋊ #8265

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₄₇
commutator, socle, prime radical	C₂³×C₄₇	C₂×C₄²
Fitting	C₂×C₄₇×#322	C₂
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#322	D₄₇
hypocenter	C₄₇	#8265
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ C₂×#322

438 conjugacy classes of subgroups.

Polycyclic presentation:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 60721);