#11928218

order	1248
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃×#261
commutator	C₂×C₃×C₁₃	C₂×C₈
Fitting, socle	C₂²×C₃×C₁₃	C₂×C₄
prime radical	C₂²×D₃₉	C₄
cosocle	C₂×C₃×Dic₁₃	C₂²
hypocenter	C₃×C₁₃	C₂²⋊C₈
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂²

100 conjugacy classes of subgroups.

μ_t(G) = 624

Polycyclic presentation:

2^5,3,13|a^2=c,b^2=e,c^2=e,b^a=bd,g^a=g^8,f^b=f^2,g^c=g^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 330);