C₁₃×#13643 #15699982

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#13643

Subgroups

	subgroup	G/H
center	C₈×C₁₃	#117
commutator	C₂×C₄	C₂²×C₈×C₁₃
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
socle	C₂×C₁₃	#2163
prime radical	C₂³×C₁₃	M₃₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃ ◁ C₁₃×#346 ◁ G

164 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 106 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)(14,15,17,24,18,25,34,50,19,26,35,49,36,51,61,72,20,23,33,46,37,47,60,70,38,22,42,44,62,45,67,69)(16,27,29,48,30,52,55,71,31,43,56,65,57,68,74,77,28,21,32,40,53,41,58,66,54,39,59,63,73,64,75,76);(14,16)(15,21)(17,32)(18,30)(19,31)(20,28)(22,43)(23,27)(24,48)(25,41)(26,39)(29,33)(34,58)(35,59)(36,57)(37,53)(38,54)(40,46)(42,56)(44,63)(45,68)(47,52)(49,65)(50,71)(51,64)(55,60)(61,75)(62,73)(66,70)(67,74)(69,76)(72,77);(15,22,23,26)(16,28)(17,33)(21,39,27,43)(24,49,46,44)(25,45,47,51)(30,53)(31,54)(34,60)(35,42)(40,65,48,63)(41,64,52,68)(50,72,70,69)(57,73)(61,67)(66,77,71,76)

Conjugacy classes & character table

832 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6631);