3₋¹⁺²×C₅₃ #13083655

order	1431
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	3₋¹⁺²×C₅₃
unambiguous semidirect product	C₉⋊(C₃×C₅₃)
unambiguous semidirect product	(C₉×C₅₃)⋊C₃

Subgroups

	subgroup	G/H
center, socle	C₃×C₅₃	C₃²
commutator, Frattini, cosocle	C₃	C₃²×C₅₃
prime radical	C₃²×C₅₃	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₅₃ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 62
transitive degree	μ_t(G) = 477

A minimal faithful permutation representation — 2 generators on 62 points:

(1,2,4,3,6,8,7,5,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62);(2,5,6)(4,8,9)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅₃×AΣL(1,𝔽₂₇), C₅₃×#731, C₅₃×#733, …
maximal normal subgroup of	C₅₃×AΣL(1,𝔽₂₇), C₅₃×#731, C₅₃×#733, …
maximal quotient of	C₅₃×C₃²⋊C₉, C₅₃×C₉⋊C₉, C₃×3₋¹⁺²×C₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1431, 4);

3−1+2×C53 #13083655