#28301463

order	13568
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

No aliases for this group.

C₅₃ ⋊ #8134

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#6157
commutator, socle, prime radical	C₂³×C₅₃	C₂×C₄²
Fitting	C₂×#97×C₅₃	C₄
cosocle	C₂×C₄×Dic₅₃	C₂³
hypercenter	C₂×#97	#6157
hypocenter	C₅₃	#8134
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

414 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.

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

μ_t(G) = 13568

Polycyclic presentation:

2^8,53|a^2=e,b^2=f,c^2=d,e^2=g,f^2=h,b^a=bd,c^a=ch,i^a=i^23,c^b=cg,i^b=i^30,i^e=i^52,i^f=i^52

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1086939);