C₁₃×#32949 #15719288

order	3328
nilpotency class	3
isoclinism	isoclinic class of #32947
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₃×#32949

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2847
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#585	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

1278 conjugacy classes of subgroups; only the 290 normal subgroups are shown.

normal subgroups only

This group has 1278 conjugacy classes of subgroups — too many to draw. Only its 290 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 — 4 generators on 77 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,25)(16,26,31,49)(17,22,34,44)(18,23,36,46)(19,37,27,24)(21,38,41,30)(28,47,54,69)(29,48,56,70)(32,57,59,42)(33,60,50,43)(35,61,51,45)(39,62,65,53)(40,63,66,55)(52,72,74,68)(58,67,71,76)(64,73,75,77);(14,16,27,38,20,31,19,30)(15,21,37,49,25,41,24,26)(17,28,50,62,34,54,33,53)(18,29,51,63,36,56,35,55)(22,39,60,69,44,65,43,47)(23,40,61,70,46,66,45,48)(32,52,71,77,59,74,58,73)(42,64,76,72,57,75,67,68);(14,17)(15,22)(16,28)(18,32)(19,33)(20,34)(21,39)(23,42)(24,43)(25,44)(26,47)(27,50)(29,52)(30,53)(31,54)(35,58)(36,59)(37,60)(38,62)(40,64)(41,65)(45,67)(46,57)(48,68)(49,69)(51,71)(55,73)(56,74)(61,76)(63,77)(66,75)(70,72);(14,18)(15,23)(16,29)(17,32)(19,35)(20,36)(21,40)(22,42)(24,45)(25,46)(26,48)(27,51)(28,52)(30,55)(31,56)(33,58)(34,59)(37,61)(38,63)(39,64)(41,66)(43,67)(44,57)(47,68)(49,70)(50,71)(53,73)(54,74)(60,76)(62,77)(65,75)(69,72)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 25937);