C₁₃×#13435 #15699774

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13432
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13435

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

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

normal subgroups only

This group has 408 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) = 77
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 77 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,25)(16,26,30,48)(17,31,35,60)(18,36,39,23)(19,40,41,24)(21,37,44,28)(22,45,47,34)(27,52,32,61)(29,56,57,51)(33,64,66,59)(38,49,70,68)(42,72,74,77)(43,55,71,69)(46,65,67,75)(50,63,76,54)(53,73,62,58);(14,16,20,30)(15,21,25,44)(17,32,35,27)(18,37,39,28)(19,29,41,57)(22,42,47,74)(23,48,36,26)(24,43,40,71)(31,58,60,73)(33,53,66,62)(34,54,45,63)(38,69,70,55)(46,76,67,50)(49,56,68,51)(52,64,61,59)(65,72,75,77);(14,17,18,33,20,35,39,66)(15,22,23,46,25,47,36,67)(16,27,28,53,30,32,37,62)(19,34,38,65,41,45,70,75)(21,42,26,50,44,74,48,76)(24,31,49,59,40,60,68,64)(29,54,55,77,57,63,69,72)(43,73,51,52,71,58,56,61)

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, 6423);