C₁₉₃⋊#401 #27135202

order	12352
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

C₁₉₃⋊#401

C₁₉₃ ⋊ #401

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₉₃
commutator, socle, prime radical, cosocle	C₂³×C₁₉₃	C₂³
Fitting	#95×C₁₉₃	C₂
hypercenter	#95	D₁₉₃
hypocenter	C₁₉₃	#401
LCS	G ▷ C₂³×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₂³ ◁ #95

118 conjugacy classes of subgroups.

Polycyclic presentation:

2^6,193|a^2=def,b^2=de,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^192

1942 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 492);