C₁₃×#9008 #15695347

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9008

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃	#120
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	#386
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

398 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 61
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 61 points:

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

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1996);