Finite Group Databasebeta

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#376×C₁₆₇ #24922777

order	10688
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₆₇ · Schur multiplier (H₂) = C₂×C₄²

Aliases

#376×C₁₆₇

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₆₇	C₂²
commutator	C₂	C₂×C₄²×C₁₆₇
Frattini, cosocle	C₂³	C₂³×C₁₆₇
socle, prime radical	C₂³×C₁₆₇	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₆₇ ◁ G

178 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6680 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36321967, #36322031, #36322622, …
maximal subgroup of	#1274×C₁₆₇, #1300×C₁₆₇, #1500×C₁₆₇, …
maximal normal subgroup of	#1274×C₁₆₇, #1300×C₁₆₇, #1500×C₁₆₇, …
maximal quotient of	C₄×#95×C₁₆₇, #1434×C₁₆₇, #1744×C₁₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10688, 57);