C₈₉×#2809 #26017283

order	11392
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

	subgroup	G/H
center, socle, prime radical	C₂³×C₈₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₈₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

368 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 192 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, 1541);