C₁₃×#13617 #15699956

order	3328
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#13617

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×D₁₆
commutator	C₁₆	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
prime radical	C₂²×C₁₃×D₁₆	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ C₂²×C₁₃×C₁₆ ◁ G

330 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 49
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(18,19)(20,26)(21,25)(22,36)(23,38)(24,29)(27,32)(28,33)(30,39)(31,45)(34,42)(35,41)(37,49)(40,46)(43,47)(44,48);(19,25)(20,23)(21,32)(22,33)(26,42)(27,28)(29,41)(30,46)(31,37)(34,47)(35,48)(36,40)(38,39)(43,49)(44,45);(18,20,24,23)(19,26,29,38)(21,30,35,34)(22,31,37,33)(25,39,41,42)(27,43,44,40)(28,36,45,49)(32,47,48,46)

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6605);