#29570448

order	15616
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₆₁ ⋊ #8135

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₆₁
commutator, socle, prime radical	C₂³×C₆₁	C₂×C₄²
Fitting	C₆₁×#1744	C₂
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	#1744	D₆₁
hypocenter	C₆₁	#8135
LCS	G ▷ C₂³×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄² ◁ #1744

382 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 179 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=e,b^2=f,c^2=d,e^2=g,f^2=h,b^a=bd,c^a=cgh,c^b=cg,i^b=i^60

2488 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 60003);