C₁₃×#12464 #15698803

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

Aliases

direct product

C₁₃×#12464

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

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, 5452);