C₁₃×#11748 #15698087

order	3328
nilpotency class	4
isoclinism	isoclinic class of #1347
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#11748

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃	#102
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#102
prime radical	C₂³×C₁₃	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

324 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 1664

A minimal faithful permutation representation — 3 generators on 53 points:

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

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4736);