C₁₃×#12893 #15699232

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12026
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#12893

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#427
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1835
prime radical	C₂³×C₁₃	#135
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₁₃×#117 ◁ C₁₃×#405 ◁ G

234 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 122 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)(17,35,38,66)(18,40)(19,24)(20,43)(21,27)(22,31)(23,37,49,69)(25,29)(26,41)(30,58,61,44)(32,53)(33,45)(34,55)(36,67,57,50)(39,70,68,48)(42,51)(46,64)(47,56)(52,60,73,77)(54,63)(59,65,75,74)(62,71,76,72);(14,16,29,56,41,63,19,32,21,34,18,31,20,33,42,64)(15,22,24,28,43,53,25,45,27,47,51,55,26,46,40,54)(17,30,57,75,68,76,37,60,38,61,36,59,39,62,69,77)(23,44,48,52,67,72,35,65,49,58,70,73,50,71,66,74);(14,17,18,36,41,68,42,69,21,38,29,57,20,39,19,37)(15,23,24,48,43,67,25,35,27,49,51,70,26,50,40,66)(16,30,31,59,63,76,64,77,34,61,56,75,33,62,32,60)(22,44,28,52,53,72,45,65,47,58,55,73,46,71,54,74)

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, 5881);