Finite Group Databasebeta

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#106×C₂₇₁ #22576027

order	8672
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₂₇₁ · Schur multiplier (H₂) = C₂

Aliases

#106×C₂₇₁

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₇₁	D₄
commutator	C₄	C₂×C₄×C₂₇₁
Frattini, cosocle	C₂×C₄	C₂²×C₂₇₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₇₁ ◁ C₂×C₄×C₂₇₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3794 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31773706, #31773719, #106×D₂₇₁, …
maximal subgroup of	#360×C₂₇₁, #365×C₂₇₁, C₂×#106×C₂₇₁, …
maximal normal subgroup of	#360×C₂₇₁, #365×C₂₇₁, C₂×#106×C₂₇₁, …
maximal quotient of	#334×C₂₇₁, #340×C₂₇₁, #365×C₂₇₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8672, 13);