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#108×C₂₆₉ #22575322

order	8608
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₂₆₉ · Schur multiplier (H₂) = C₁

Aliases

#108×C₂₆₉

Subgroups

	subgroup	G/H
center	C₄×C₂₆₉	D₄
commutator	C₄	C₂×C₄×C₂₆₉
Frattini, cosocle	C₂×C₄	C₂²×C₂₆₉
socle	C₂×C₂₆₉	C₄⋊C₄
prime radical	C₂²×C₂₆₉	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₆₉ ◁ C₂×C₄×C₂₆₉ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3766 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31770411, #31770417, #31770420, …
maximal subgroup of	#359×C₂₆₉, #361×C₂₆₉, #362×C₂₆₉, …
maximal normal subgroup of	#359×C₂₆₉, #361×C₂₆₉, #362×C₂₆₉, …
maximal quotient of	#334×C₂₆₉, #335×C₂₆₉, #341×C₂₆₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8608, 15);