C₃₁×#62694 #21519453

order	7936
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₃₁ · Schur multiplier (H₂) = C₂¹³

Aliases

	subgroup	G/H
center	C₄²×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
socle	C₂²×C₃₁	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₃₁ ◁ G

6640 conjugacy classes of subgroups; only the 5670 normal subgroups are shown.

normal subgroups only

This group has 6640 conjugacy classes of subgroups — too many to draw. Only its 5670 normal subgroups are shown.

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

2356 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7936, 55682);