D₄×Q₈×C₁₆₇ #24922950

order	10688
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₆₇ · Schur multiplier (H₂) = C₂⁵

Aliases

D₄×Q₈×C₁₆₇

	subgroup	G/H
center, socle	C₂²×C₁₆₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₁₆₇
prime radical	C₂×D₄×C₁₆₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₆₇ ◁ G

280 conjugacy classes of subgroups.

4175 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10688, 230);