C₁₃×#9977 #15696316

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9974
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9977

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₁₃×#3186	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

544 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 102 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)(16,19)(17,20)(18,21)(22,25)(23,26)(24,28)(27,29)(30,31)(32,39)(33,36)(34,38)(35,41)(37,43)(40,45)(42,44);(14,16,18,23)(15,19,21,26)(17,22,24,29)(20,27,28,25)(30,32,34,42)(31,35,38,45)(33,40,43,41)(36,39,37,44);(14,17)(15,20)(16,22)(18,24)(19,25)(21,28)(23,29)(26,27)(31,36)(32,40)(33,43)(37,38)(39,44)(41,42)

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, 2965);