C₉×C₅₃×AΣL(1,𝔽₂₇) #50311601

order	38637
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉×C₅₃ · Schur multiplier (H₂) = C₃³

Aliases

direct product

C₉×C₅₃×AΣL(1,𝔽₂₇)

Subgroups

	subgroup	G/H
center	C₃×C₉×C₅₃	H(3,𝔽₃)
commutator	C₃²	C₃²×C₉×C₅₃
Frattini, cosocle	C₃³	C₃³×C₅₃
socle	C₃²×C₅₃	C₃×H(3,𝔽₃)
prime radical	C₃×C₅₃×AΣL(1,𝔽₂₇)	C₃
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₅₃ ◁ C₃²×C₉×C₅₃ ◁ G

472 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 4293

A minimal faithful permutation representation — 3 generators on 71 points:

(1,2,4,3,5,7,6,8,9)(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);(10,11,13)(12,14,17)(15,18,16);(11,14,15)

Conjugacy classes & character table

8109 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38637, 276);