#11928222

order	1248
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂	(C₂×D₃)⋊#261
commutator, Fitting, prime radical	C₂²×C₃×C₁₃	C₂×C₄
Frattini, hypercenter	C₂²	D₃×#261
socle	C₂×C₃×C₁₃	C₂²⋊C₄
cosocle	C₂×C₃×Dic₁₃	C₂²
hypocenter	C₃×C₁₃	#101
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₂²

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 624

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 334);