C₁₃×#13648 #15699987

order	3328
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13648

Subgroups

	subgroup	G/H
center	C₁₃×C₁₆	C₂×D₄
commutator	C₄	C₂²×C₁₃×C₁₆
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
socle	C₂×C₁₃	D₄×C₁₆
prime radical	C₁₃×#135	C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₃×C₁₆ ◁ C₂×C₁₃×C₃₂ ◁ G

184 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 118 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)(14,15,19,26,20,27,44,59,21,25,45,57,47,58,50,75,22,28,46,60,48,30,62,64,18,40,42,71,43,63,68,74)(16,29,32,61,33,38,66,70,31,23,49,51,65,39,24,54,34,52,56,76,67,36,55,69,41,53,72,77,73,17,35,37);(14,16)(15,23)(17,30)(18,41)(19,32)(20,33)(21,31)(22,34)(24,50)(25,52)(26,51)(27,39)(28,53)(29,40)(35,68)(36,58)(37,64)(38,63)(42,72)(43,73)(44,66)(45,49)(46,56)(47,65)(48,67)(54,59)(55,62)(57,76)(60,77)(61,71)(69,75)(70,74);(14,17,19,37,20,29,44,61,21,38,45,70,47,23,50,51,22,39,46,54,48,52,62,76,18,36,42,69,43,53,68,77)(15,24,26,34,27,56,59,67,25,55,57,41,58,72,75,73,28,35,60,16,30,32,64,33,40,66,71,31,63,49,74,65)

Conjugacy classes & character table

1144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6636);