C₂³×C₃₁×#120 #21519414

order	7936
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₃₁ · Schur multiplier (H₂) = C₂¹⁶

Aliases

C₂³×C₃₁×#120

	subgroup	G/H
center, socle	C₂⁵×C₃₁	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵×C₃₁ ◁ G

42862 conjugacy classes of subgroups; only the 7902 normal subgroups are shown.

normal subgroups only

This group has 42862 conjugacy classes of subgroups — too many to draw. Only its 7902 normal subgroups are shown.

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

3472 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7936, 55643);