C₁₃×#10217 #15696556

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10217

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#127
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

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

normal subgroups only

This group has 430 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) = 832

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

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3205);