D₄×Q₁₆×C₈₉ #26017760

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

Aliases

D₄×Q₁₆×C₈₉

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

472 conjugacy classes of subgroups.

3115 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 2018);