C₁₉₃⋊#564 #27136014

order	12352
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁴

Aliases

C₁₉₃⋊#564

C₁₉₃ ⋊ #564

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₉₃
commutator, socle, prime radical, cosocle	C₂²×C₁₉₃	C₂⁴
Fitting	#125×C₁₉₃	C₂
hypercenter	#125	D₁₉₃
hypocenter	C₁₉₃	#564
LCS	G ▷ C₂²×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₂² ◁ #125

172 conjugacy classes of subgroups.

Polycyclic presentation:

2^6,193|a^2=e,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,g^d=g^192

1363 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 1304);