C₁₃×#8746 #15695085

order	3328
nilpotency class	3
isoclinism	isoclinic class of #8746
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#8746

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#381
commutator	C₂⁴	C₂²×C₄×C₁₃
Frattini, cosocle	C₂⁵	C₂³×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂⁵×C₁₃ ◁ G

814 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 118 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 — 3 generators on 37 points:

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

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1734);