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#95×C₂₄₁ #21440498

order	7712
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄²×C₂₄₁ · Schur multiplier (H₂) = C₂³

Aliases

#95×C₂₄₁

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₄₁	C₂²
commutator	C₂	C₄²×C₂₄₁
Frattini, cosocle	C₂³	C₂²×C₂₄₁
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₄₁ ◁ G

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4820 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#29507450, #29507453, #95×D₂₄₁, …
maximal subgroup of	#327×C₂₄₁, #328×C₂₄₁, C₂×#95×C₂₄₁, …
maximal normal subgroup of	#327×C₂₄₁, #328×C₂₄₁, C₂×#95×C₂₄₁, …
maximal quotient of	#336×C₂₄₁, H(3,ℤ/4)×C₂₄₁, #338×C₂₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7712, 2);