#27134978

order	12352
automorphism	?
homology	Abelianization (H₁) = C₆₄ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

C₁₉₃ ⋊ C₆₄

	subgroup	G/H
center, Frattini, hypercenter	C₃₂	D₁₉₃
commutator, hypocenter	C₁₉₃	C₆₄
Fitting, cosocle	C₃₂×C₁₉₃	C₂
socle, prime radical	C₂×C₁₉₃	C₃₂
LCS	G ▷ C₁₉₃
UCS	C₁ ◁ C₃₂

14 conjugacy classes of subgroups.

Polycyclic presentation:

2^6,193|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^192

3136 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 268);