C₂×C₅₉×#392 #21420702

order	7552
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅₉ · Schur multiplier (H₂) = C₂⁸

Aliases

C₂×C₅₉×#392

	subgroup	G/H
center, socle	C₂⁴×C₅₉	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₅₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅₉ ◁ G

1812 conjugacy classes of subgroups; only the 360 normal subgroups are shown.

normal subgroups only

This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.

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

2596 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7552, 1116);