C₁₃×#13431 #15699770

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13429
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13431

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

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

normal subgroups only

This group has 402 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)(16,26,30,47)(17,31,35,49)(18,36,39,23)(19,24,41,50)(21,37,44,28)(22,40,46,34)(27,53,32,62)(29,52,58,76)(33,64,66,61)(38,60,67,48)(42,71,73,77)(43,69,74,56)(45,65,68,70)(51,57,75,55)(54,72,63,59);(14,16,20,30)(15,21,25,44)(17,32,35,27)(18,37,39,28)(19,29,41,58)(22,42,46,73)(23,47,36,26)(24,43,50,74)(31,59,49,72)(33,54,66,63)(34,55,40,57)(38,69,67,56)(45,75,68,51)(48,76,60,52)(53,64,62,61)(65,71,70,77);(14,17,18,33,20,35,39,66)(15,22,23,45,25,46,36,68)(16,27,28,54,30,32,37,63)(19,40,38,70,41,34,67,65)(21,42,26,51,44,73,47,75)(24,49,48,64,50,31,60,61)(29,57,56,71,58,55,69,77)(43,59,52,62,74,72,76,53)

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, 6419);