#97×C₆₇ #14523901

order	2144
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄²×C₆₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

#97×C₆₇

Subgroups

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²
commutator	C₂	C₄²×C₆₇
Frattini, cosocle	C₂×C₄	C₂²×C₆₇
socle, prime radical	C₂²×C₆₇	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 2144

A minimal faithful permutation representation — 2 generators on 79 points:

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

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	#16863135, #16863137, #16863174, …
maximal subgroup of	#329×C₆₇, #330×C₆₇, #347×C₆₇, …
maximal normal subgroup of	#329×C₆₇, #330×C₆₇, #347×C₆₇, …
maximal quotient of	#322×C₆₇, #336×C₆₇, #347×C₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2144, 4);

#97×C67 #14523901