C₃×C₉×3₋¹⁺²×C₅₃ #50311745

order	38637
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₃³×C₉×C₅₃ · Schur multiplier (H₂) = C₃⁵

Aliases

direct product

C₃×C₉×3₋¹⁺²×C₅₃

Subgroups

	subgroup	G/H
center	C₃²×C₉×C₅₃	C₃²
commutator	C₃	C₃³×C₉×C₅₃
Frattini, cosocle	C₃²	C₃⁴×C₅₃
socle	C₃³×C₅₃	C₃³
prime radical	C₃⁴×C₅₃	C₃²
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₉×C₅₃ ◁ G

1148 conjugacy classes of subgroups; only the 872 normal subgroups are shown.

normal subgroups only

This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 872 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) = 74
transitive degree	μ_t(G) = 12879

A minimal faithful permutation representation — 4 generators on 74 points:

(1,2,3)(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);(4,5,7,6,8,10,9,11,12);(13,14,16,15,18,20,19,17,21);(14,17,18)(16,20,21)

Conjugacy classes & character table

15741 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38637, 420);