C₅₉⋊#17309 #28554253

order	15104
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₅₉
commutator, socle, prime radical, cosocle	C₂⁴×C₅₉	C₂⁴
Fitting	C₅₉×#1446	C₂
hypercenter	#1446	D₅₉
hypocenter	C₅₉	#17309
LCS	G ▷ C₂⁴×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂⁴ ◁ #1446

1466 conjugacy classes of subgroups; only the 283 normal subgroups are shown.

normal subgroups only

This group has 1466 conjugacy classes of subgroups — too many to draw. Only its 283 normal subgroups are shown.

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

μ_t(G) = 15104

Polycyclic presentation:

2^8,59|a^2=h,b^2=g,c^2=g,d^2=h,b^a=be,c^a=cf,d^a=dh,c^b=cg,d^b=def,d^c=de,i^d=i^58

1322 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 135132);