C₁₃×#9334 #15695673

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9331
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9334

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

398 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 832

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

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

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 2322);