C₁₃×#10210 #15696549

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10208
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10210

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

440 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 832

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

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

Conjugacy classes & character table

325 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3198);