C₁₃×#62849 #15749188

order	3328
nilpotency class	2
isoclinism	isoclinic class of #62842
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₃ · Schur multiplier (H₂) = C₂¹³

Aliases

direct product

C₁₃×#62849

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

6578 conjugacy classes of subgroups; only the 6270 normal subgroups are shown.

normal subgroups only

This group has 6578 conjugacy classes of subgroups — too many to draw. Only its 6270 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) = 53
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 6 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,19)(16,20,21,18)(23,28)(26,38)(29,32)(30,39)(34,48)(37,49)(41,44)(47,53);(14,16,17,21)(15,18,19,20)(25,36)(30,39)(33,46)(37,49)(41,44)(43,50)(47,53)(51,52);(22,23,27,28)(24,32,35,29)(25,30,36,39)(26,31,38,40)(33,44,46,41)(34,45,48,42)(37,43,49,50)(47,52,53,51);(22,24,27,35)(23,29,28,32)(25,33,36,46)(26,34,38,48)(30,41,39,44)(31,42,40,45)(37,47,49,53)(43,51,50,52);(22,25)(23,30)(24,33)(26,37)(27,36)(28,39)(29,41)(31,43)(32,44)(34,47)(35,46)(38,49)(40,50)(42,51)(45,52)(48,53);(22,26)(23,31)(24,34)(25,37)(27,38)(28,40)(29,42)(30,43)(32,45)(33,47)(35,48)(36,49)(39,50)(41,51)(44,52)(46,53)

Conjugacy classes & character table

1066 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 55837);