C₁₃×#9992 #15696331

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9986
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9992

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₁₃×#3192	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

562 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 45
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 45 points:

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

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, 2980);