#34034477

order	18688
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#10596842
commutator, socle, prime radical	C₂²×C₇₃	C₂²×C₁₆
Fitting	C₄⋊C₈×C₇₃	C₈
cosocle	C₂×#11924031	C₂³
hypercenter	C₄⋊C₈	#10596842
hypocenter	C₇₃	#13660
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

158 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.

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

μ_t(G) = 18688

Polycyclic presentation:

2^8,73|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,g^2=h,b^a=bd,c^a=ch,i^a=i^63,i^b=i^72,i^c=i^10,i^e=i^27,i^f=i^72

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1118061);