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#347×C₁₆₇ #24922748

order	10688
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₆₇ · Schur multiplier (H₂) = C₁

Aliases

#347×C₁₆₇

Subgroups

	subgroup	G/H
center	C₄×C₁₆₇	C₄²
commutator	C₄	C₄²×C₁₆₇
Frattini, cosocle	C₂×C₈	C₂²×C₁₆₇
socle	C₂×C₁₆₇	#97
prime radical	C₂²×C₁₆₇	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₆₇ ◁ G

46 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3674 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36322170, #36322172, #347×D₁₆₇, …
maximal subgroup of	#1355×C₁₆₇, #1356×C₁₆₇, C₂×#347×C₁₆₇, …
maximal normal subgroup of	#1355×C₁₆₇, #1356×C₁₆₇, C₂×#347×C₁₆₇, …
maximal quotient of	#1313×C₁₆₇, #1375×C₁₆₇, C₂×#347×C₁₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10688, 28);