C₂×#509×C₈₉ #26017886

order	11392
nilpotency class	4
isoclinism	isoclinic class of #509
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈₉ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×#509×C₈₉

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×D₈
commutator, Frattini, cosocle	C₈	C₂⁴×C₈₉
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×C₄×C₈₉ ◁ C₂²×C₈×C₈₉ ◁ G

400 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.

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

2848 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 2144);