#30607300

order	15616
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#6923
commutator, socle, prime radical	C₂³×C₆₁	C₂²×C₈
Fitting	C₂×#97×C₆₁	C₄
cosocle	C₂²×#92418	C₂³
hypercenter	C₂×#97	#6923
hypocenter	C₆₁	#12880
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

322 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.

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

μ_t(G) = 15616

Polycyclic presentation:

2^8,61|a^2=f,b^2=e,c^2=d,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^11,c^b=ch,i^b=i^60,i^f=i^60

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1096855);