#29707429

order	15616
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	#120×D₆₁
commutator, prime radical, cosocle	C₂⁴×C₆₁	C₂⁴
Frattini	C₂⁴	C₂³×D₆₁
Fitting	C₆₁×#2030	C₂
socle	C₂²×C₆₁	C₂×#120
hypercenter	#2030	D₆₁
hypocenter	C₆₁	#23470
LCS	G ▷ C₂⁴×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #2030

1178 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.

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

μ_t(G) = 3904

Polycyclic presentation:

2^8,61|a^2=e,b^2=e,c^2=h,d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,f^b=fh,d^c=dh,i^d=i^60

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 196984);