C₄₇×#10015 #26049713

order	12032
nilpotency class	3
isoclinism	isoclinic class of #10012
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄₇ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center	C₂×C₄×C₄₇	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₄₇
socle	C₂²×C₄₇	#392
prime radical	C₄₇×#2397	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

696 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

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

1880 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 3003);