#11927990

order	1248
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₃×D₁₃
commutator	C₂×C₃×C₁₃	C₂×C₈
Fitting, cosocle	C₂×C₃×C₄×C₁₃	C₂²
socle, prime radical	C₂²×C₃×C₁₃	C₂×C₄
hypocenter	C₃×C₁₃	C₄⋊C₈
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₄

76 conjugacy classes of subgroups.

μ_t(G) = 1248

Polycyclic presentation:

2^5,3,13|a^2=d,b^2=c,c^2=e,b^a=bd,g^a=g^12,f^b=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 102);