C₆₁×#15155 #29518588

order	15616
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₆₁ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

	subgroup	G/H
center, socle	C₂⁴×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₆₁
prime radical	C₂³×D₄×C₆₁	C₂²
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₁ ◁ G

2158 conjugacy classes of subgroups; only the 558 normal subgroups are shown.

normal subgroups only

This group has 2158 conjugacy classes of subgroups — too many to draw. Only its 558 normal subgroups are shown.

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

μ_t(G) = 7808

3904 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 8143);