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#117×C₂₆₉ #22575331

order	8608
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₆₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

#117×C₂₆₉

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₆₉	C₂²
commutator	C₂	C₂²×C₄×C₂₆₉
Frattini, cosocle	C₂²	C₂³×C₂₆₉
socle	C₂²×C₂₆₉	C₂³
prime radical	C₂³×C₂₆₉	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₆₉ ◁ G

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5380 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31770361, #31770364, #31770375, …
maximal subgroup of	H(3,ℤ/4)×C₂₆₉, #339×C₂₆₉, #344×C₂₆₉, …
maximal normal subgroup of	H(3,ℤ/4)×C₂₆₉, #339×C₂₆₉, #344×C₂₆₉, …
maximal quotient of	#376×C₂₆₉, C₄×C₂²⋊C₄×C₂₆₉, C₄×C₄⋊C₄×C₂₆₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8608, 24);