C₂×#464×C₈₉ #26017508

order	11392
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈₉ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×#464×C₈₉

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

500 conjugacy classes of subgroups.

3382 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 1766);