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#95×C₂₇₁ #22576016

order	8672
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄²×C₂₇₁ · Schur multiplier (H₂) = C₂³

Aliases

#95×C₂₇₁

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₇₁	C₂²
commutator	C₂	C₄²×C₂₇₁
Frattini, cosocle	C₂³	C₂²×C₂₇₁
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₇₁ ◁ G

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5420 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31773630, #31773633, #95×D₂₇₁, …
maximal subgroup of	#327×C₂₇₁, #328×C₂₇₁, C₂×#95×C₂₇₁, …
maximal normal subgroup of	#327×C₂₇₁, #328×C₂₇₁, C₂×#95×C₂₇₁, …
maximal quotient of	#336×C₂₇₁, H(3,ℤ/4)×C₂₇₁, #338×C₂₇₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8672, 2);