C₂₉×D₁₂₈ #20302451

order	7424
nilpotency class	7
isoclinism	isoclinic class of D₁₂₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

C₂₉×D₁₂₈

	subgroup	G/H
center, socle	C₂×C₂₉	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₂₉
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₄×C₂₉ ◁ C₈×C₂₉ ◁ C₁₆×C₂₉ ◁ C₂₉×C₃₂ ◁ C₂₉×C₆₄ ◁ G

46 conjugacy classes of subgroups.

1943 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7424, 539);