C₁₃×#8754 #15695093

order	3328
nilpotency class	3
isoclinism	isoclinic class of #8746
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#8754

Subgroups

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

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

normal subgroups only

This group has 566 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) = 53
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20,21,18)(17,19)(22,23,26,31,27,30,40,45)(24,32,34,46,35,28,39,42)(25,36,38,50,37,29,43,44)(33,41,49,52,48,47,51,53);(22,24,27,35)(23,28,30,32)(25,33,37,48)(26,39,40,34)(29,41,36,47)(31,46,45,42)(38,51,43,49)(44,53,50,52);(14,16,17,21)(15,18,19,20)(22,25)(23,29,30,36)(24,33)(26,38)(27,37)(28,41,32,47)(31,44,45,50)(34,49)(35,48)(39,51)(40,43)(42,52,46,53)

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, 1742);