C₁₃×#11771 #15698110

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11769
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#11771

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1505
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₃
prime radical	C₂³×C₁₃	AGL(1,ℤ/8)
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

292 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 94 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)(16,27,30,56)(17,23)(18,38,40,54)(19,25)(20,43)(21,26)(22,29)(24,41,52,42)(28,55,58,73)(31,51,32,62)(33,63,59,77)(34,65,66,75)(35,49)(36,69)(37,50)(39,53)(44,57)(45,60)(46,61)(47,64)(48,67,74,68)(70,72)(71,76);(14,16,21,30)(15,22,26,46)(17,33,37,59)(18,39,40,60)(19,32,20,31)(23,47,50,72)(24,51,52,62)(25,53,43,45)(27,54,56,38)(28,36,58,35)(29,41,61,42)(34,57,66,76)(44,69,71,49)(48,73,74,55)(63,75,77,65)(64,67,70,68);(14,17,20,36,21,37,19,35)(15,23,43,69,26,50,25,49)(16,28,32,59,30,58,31,33)(18,34,42,68,40,66,41,67)(22,44,53,72,46,71,45,47)(24,48,54,75,52,74,38,65)(27,55,62,77,56,73,51,63)(29,57,39,70,61,76,60,64)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4759);