C₁₃×#13630 #15699969

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×#13630

Subgroups

	subgroup	G/H
center	C₁₃×C₁₆	C₂×D₄
commutator	C₄	C₂²×C₁₃×C₁₆
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
socle	C₂×C₁₃	C₂×C₄⋊C₁₆
prime radical	C₂³×C₁₃	M₃₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₃×C₁₆ ◁ C₂²×C₁₃×C₁₆ ◁ G

198 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 154 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)(14,15,18,24,19,25,36,47,20,23,37,45,39,46,62,68,21,26,38,48,40,49,63,69,17,33,34,59,35,60,61,75)(16,27,30,51,31,52,56,72,32,42,57,65,58,66,74,76,28,50,53,70,54,71,73,77,29,22,41,43,55,44,64,67);(14,16,17,29,21,28,20,32)(15,22,23,27,26,42,33,50)(18,30,34,41,38,53,37,57)(19,31,35,55,40,54,39,58)(24,43,45,51,48,65,59,70)(25,44,46,52,49,66,60,71)(36,56,61,64,63,73,62,74)(47,67,68,72,69,76,75,77);(16,28)(22,42)(27,50)(29,32)(30,53)(31,54)(41,57)(43,65)(44,66)(51,70)(52,71)(55,58)(56,73)(64,74)(67,76)(72,77)

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, 6618);