C₁₃×#10390 #15696729

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10390
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#10390

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#393
commutator, Frattini, cosocle	C₂⁵	C₂³×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂⁵×C₁₃ ◁ G

762 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 90 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)(16,18)(17,19)(20,21)(22,23)(24,27)(25,32,34,28)(26,29)(30,37,33,35)(31,36);(14,16)(15,18)(17,20)(19,21)(22,24)(23,27)(25,33,34,30)(26,31)(28,35,32,37)(29,36);(18,21)(22,25)(23,28)(24,30)(26,34)(27,35)(29,32)(31,33)(36,37)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3378);