C₁₃×#23467 #15709806

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₃×#23467

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃	#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×#120
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

1378 conjugacy classes of subgroups; only the 334 normal subgroups are shown.

normal subgroups only

This group has 1378 conjugacy classes of subgroups — too many to draw. Only its 334 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) = 37
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 4 generators on 37 points:

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

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 16455);