C₁₃×#12463 #15698802

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12463
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#12463

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1675
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₃
prime radical	C₁₃×#135	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₈×C₁₃ ◁ G

172 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 74 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)(14,15,21,27)(16,28,33,60)(17,34)(18,39,41,25)(19,24,43,55)(20,44,40,26)(22,45,49,30)(23,50)(29,61)(31,58,68,48)(32,47,66,59)(35,54)(36,70)(37,56)(38,51)(42,52)(46,63)(53,71)(57,72)(62,69)(64,74)(65,73)(67,76)(75,77);(14,16,19,31,20,32,41,45,21,33,43,68,40,66,18,30)(15,22,39,59,26,48,55,60,27,49,25,47,44,58,24,28)(17,29,42,67,36,63,50,72,38,65,71,77,37,64,35,62)(23,46,70,76,52,61,34,69,54,74,56,75,53,73,51,57);(14,17)(15,23)(16,29)(18,35)(19,42)(20,36)(21,38)(22,46)(24,51)(25,56)(26,52)(27,54)(28,57)(30,62)(31,67)(32,63)(33,65)(34,55)(37,40)(39,70)(41,50)(43,71)(44,53)(45,72)(47,75)(48,61)(49,74)(58,73)(59,76)(60,69)(64,66)(68,77)

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5451);