C₈₉×#3444 #26017918

order	11392
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₈₉ · Schur multiplier (H₂) = C₂⁸

Aliases

	subgroup	G/H
center	C₄²×C₈₉	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₈₉
socle	C₂²×C₈₉	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₈₉ ◁ G

1212 conjugacy classes of subgroups.

4984 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 2176);