C₁₃×#10428 #15696767

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#10428

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 3328

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

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

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, 3416);