C₁₉×#10624561 #28352757

order	13851
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉×C₁₉ · Schur multiplier (H₂) = C₃×C₉

Aliases

direct product

C₁₉×#10624561

Subgroups

	subgroup	G/H
center, socle, prime radical	C₃³×C₁₉	C₃³
commutator	C₃²	C₃²×C₉×C₁₉
Frattini, cosocle	C₃³	C₃³×C₁₉
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₁₉ ◁ G

374 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 206 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) = 46
transitive degree	μ_t(G) = 13851

A minimal faithful permutation representation — 3 generators on 46 points:

(2,4,7)(5,9,8)(11,13,16)(14,18,17)(19,20,23,22,24,27,21,25,26)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46);(1,2,5,3,4,8,6,7,9)(20,24,25)(23,26,27);(10,11,14,12,13,17,15,16,18)

Conjugacy classes & character table

2907 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 121);