C₁₃×#12398 #15698737

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#12398

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₃
prime radical	C₂×D₄×C₁₃	D₈
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ C₈×D₄×C₁₃ ◁ G

286 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 61
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,23)(16,24,27,28)(17,22,18,21)(20,26,29,25)(30,31,35,39)(32,40,43,59)(33,44,48,58)(34,49,46,38)(36,51,53,41)(37,54,56,47)(42,60,50,55)(45,57,61,52);(14,16,19,27)(15,20,23,29)(17,26,18,25)(21,28,22,24)(30,32,35,43)(31,36,39,53)(33,45,48,61)(34,50,46,42)(37,55,56,60)(38,57,49,52)(40,58,59,44)(41,54,51,47);(15,21)(17,18)(20,28)(22,23)(24,29)(25,26)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5386);