C₁₃×#13438 #15699777

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13436
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13438

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

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

normal subgroups only

This group has 406 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)(14,15,21,26)(16,27,32,52)(17,33,38,66)(18,39,20,24)(19,41,43,25)(22,31,47,29)(23,48,51,36)(28,57,60,77)(30,62,42,56)(34,67,58,73)(35,65,37,64)(40,53,44,55)(45,68,74,75)(46,61,54,63)(49,72,76,59)(50,69,71,70);(14,16,21,32)(15,22,26,47)(17,34,38,58)(18,31,20,29)(19,42,43,30)(23,49,51,76)(24,52,39,27)(25,54,41,46)(28,35,60,37)(33,57,66,77)(36,68,48,75)(40,61,44,63)(45,71,74,50)(53,56,55,62)(59,69,72,70)(64,73,65,67);(14,17,18,35,21,38,20,37)(15,23,24,50,26,51,39,71)(16,28,29,58,32,60,31,34)(19,36,40,69,43,48,44,70)(22,45,27,49,47,74,52,76)(25,33,53,64,41,66,55,65)(30,59,61,75,42,72,63,68)(46,73,56,57,54,67,62,77)

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, 6426);