#26244412

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂×C₄	#13093992
commutator, prime radical, cosocle	C₂⁴×C₄₇	C₂⁴
Frattini	C₂⁴	C₂³×D₄₇
Fitting	C₄₇×#2296	C₂
socle	C₂²×C₄₇	C₂×#120
hypercenter	#2296	D₄₇
hypocenter	C₄₇	#23564
LCS	G ▷ C₂⁴×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #2296

1162 conjugacy classes of subgroups.

Polycyclic presentation:

2^8,47|a^2=e,b^2=e,c^2=e,d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,f^b=fh,i^b=i^46

1340 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 197702);