C₁₃×#13544 #15699883

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#13544

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#482
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#2101
prime radical	C₂³×C₁₃	#137
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

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

normal subgroups only

This group has 212 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) = 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)(16,28,31,56)(17,23,35,50)(18,24)(19,27)(20,25)(21,26)(22,30,46,42)(29,58)(32,52,63,76)(33,65)(34,48,43,57)(36,49,68,75)(37,51)(38,55)(39,70,69,45)(40,53,59,77)(41,54)(44,62)(47,64)(60,72)(61,71)(66,74)(67,73);(14,16,21,42,19,31,18,30)(15,22,24,28,27,46,26,56)(17,33,43,64,35,67,34,66)(20,39,41,32,38,69,37,63)(23,47,48,65,50,74,57,73)(25,52,51,70,55,76,54,45)(29,59,62,68,61,40,60,36)(44,53,58,75,72,77,71,49);(14,17,18,34,19,35,21,43)(15,23,24,48,27,50,26,57)(16,29,30,60,31,61,42,62)(20,40,37,68,38,59,41,36)(22,44,28,58,46,72,56,71)(25,53,51,75,55,77,54,49)(32,64,39,33,63,66,69,67)(45,73,52,47,70,65,76,74)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6532);