#131×C₆₇ #14523935

order	2144
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₆₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

#131×C₆₇

Subgroups

	subgroup	G/H
center	C₈×C₆₇	C₂²
commutator	C₂	C₂²×C₄×C₆₇
Frattini, cosocle	C₄	C₂³×C₆₇
socle	C₂×C₆₇	C₂²×C₄
prime radical	#41×C₆₇	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₆₇ ◁ G

62 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 1072

A minimal faithful permutation representation — 3 generators on 83 points:

(1,2,4,7,5,8,11,14)(3,6,10,13,9,12,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(1,3)(2,6)(4,10)(5,9)(7,13)(8,12)(11,15)(14,16);(3,9)(6,12)(10,15)(13,16)

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#16863180, #16863511, #16863516, …
maximal subgroup of	#350×C₆₇, #443×C₆₇, #444×C₆₇, …
maximal normal subgroup of	#350×C₆₇, #443×C₆₇, #444×C₆₇, …
maximal quotient of	#405×C₆₇, #408×C₆₇, #424×C₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2144, 38);

#131×C67 #14523935