Q₈×Q₁₆×C₈₉ #26017856

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

Aliases

Q₈×Q₁₆×C₈₉

	subgroup	G/H
center, socle, prime radical	C₂²×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄×Q₈×C₈₉ ◁ G

336 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 2114);