#17982703

order	4352
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂³	C₂²×#3633
commutator, socle, prime radical	C₂³×C₁₇	C₂²×C₈
Fitting	C₂²×Q₈×C₁₇	C₈
cosocle	C₂²×#3624	C₂³
hypercenter	C₂²×Q₈	#3633
hypocenter	C₁₇	#13264
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

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

μ_t(G) = 4352

Polycyclic presentation:

2^8,17|a^2=f,b^2=def,c^2=e,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^8,c^b=ch,i^b=i^9,i^c=i^16,i^f=i^13,i^g=i^16

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1117947);