C₅₃×#732 #16864296

order	4293
nilpotency class	3
isoclinism	isoclinic class of AΣL(1,𝔽₂₇)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅₃ · Schur multiplier (H₂) = C₃²

Aliases

direct product

C₅₃×#732

Subgroups

	subgroup	G/H
center, socle	C₃×C₅₃	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃²×C₅₃
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₅₃ ◁ C₃²×C₅₃ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 80
transitive degree	μ_t(G) = 1431

A minimal faithful permutation representation — 2 generators on 80 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅₃×#6878, C₅₃×#6879, C₅₃×#6881, …
maximal normal subgroup of	C₅₃×#6878, C₅₃×#6879, C₅₃×#6881, …
maximal quotient of	C₅₃×#6856, C₅₃×#6859, C₅₃×#6861, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4293, 9);

C53×#732 #16864296