C₁₃×#10045 #15696384

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10038
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10045

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

444 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 98 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)(16,22)(17,25)(18,21)(19,24)(20,27)(23,29)(26,28)(30,31,36,41)(32,42,45,53)(33,38,49,56)(34,40,35,39)(37,46,52,44)(43,58,59,54)(47,61,60,51)(48,57,50,55);(19,28)(22,29)(30,32,36,45)(31,37,41,52)(33,47,49,60)(34,46,35,44)(38,54,56,58)(39,53,40,42)(43,50,59,48)(51,57,61,55);(14,16)(15,19)(17,26)(18,23)(20,29)(21,28)(22,25)(24,27)(30,33,36,49)(31,38,41,56)(32,43,45,59)(34,48,35,50)(37,51,52,61)(39,55,40,57)(42,54,53,58)(44,47,46,60)

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3033);