#32025584

order	18176
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	#120×D₇₁
commutator, prime radical, cosocle	C₂⁴×C₇₁	C₂⁴
Frattini	C₂⁴	C₂³×D₇₁
Fitting	C₇₁×#2062	C₂
socle	C₂²×C₇₁	C₂×#120
hypercenter	#2062	D₇₁
hypocenter	C₇₁	#23564
LCS	G ▷ C₂⁴×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #2062

1162 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1162 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.

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

μ_t(G) = 4544

Polycyclic presentation:

2^8,71|a^2=e,b^2=e,c^2=e,d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,f^b=fh,i^d=i^70

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 197700);