#16780291

order	3328
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₃ ⋊ #8135

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#261
commutator, socle, prime radical	C₂³×C₁₃	C₂×C₄²
Fitting	C₁₃×#336	C₄
cosocle	C₂×C₄×Dic₁₃	C₂³
hypercenter	#336	#261
hypocenter	C₁₃	#8135
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #336

382 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 3328

Polycyclic presentation:

2^8,13|a^2=e,b^2=f,c^2=d,e^2=g,f^2=h,b^a=bd,c^a=cgh,i^a=i^8,c^b=cg,i^e=i^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1086940);