C₁₃×#10227 #15696566

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10227

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#127
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

466 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 122 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)(15,19)(16,20)(17,21)(22,23,28,33)(24,34,37,45)(25,30,41,48)(26,32,27,31)(29,38,44,36)(35,50,51,46)(39,53,52,43)(40,49,42,47);(14,15,18,16)(17,20,21,19)(22,24,28,37)(23,29,33,44)(25,39,41,52)(26,38,27,36)(30,46,48,50)(31,45,32,34)(35,42,51,40)(43,49,53,47);(14,16,18,15)(17,19,21,20)(22,25,28,41)(23,30,33,48)(24,35,37,51)(26,40,27,42)(29,43,44,53)(31,47,32,49)(34,46,45,50)(36,39,38,52)

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, 3215);