C₁₃×#13342 #15699681

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13342

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₁₃×#3150	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

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

normal subgroups only

This group has 558 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) = 49
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 49 points:

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

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, 6330);