C₄₇×#15155 #26054853

order	12032
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄₇ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ 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.

3008 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 8143);