D₄×Q₈×C₁₀₉ #20294707

order	6976
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₉ · Schur multiplier (H₂) = C₂⁵

Aliases

D₄×Q₈×C₁₀₉

	subgroup	G/H
center, socle	C₂²×C₁₀₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₁₀₉
prime radical	C₂×D₄×C₁₀₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₉ ◁ G

280 conjugacy classes of subgroups.

2725 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6976, 230);