C₁₃×#10385 #15696724

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10382
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#10385

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#393
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

396 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 90 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)(14,15,17,20)(16,22)(18,21,26,28)(19,27)(23,24)(25,29)(30,31)(32,35)(33,40,42,36)(34,37)(38,43,41,45)(39,44);(14,15)(16,23,25,19)(17,20)(18,21)(22,24,29,27)(26,28)(30,32,34,39)(31,35,37,44)(33,41)(36,45)(38,42)(40,43);(14,16)(15,19)(17,25)(18,27)(20,23)(21,29)(22,28)(24,26)(30,33,34,42)(31,36,37,40)(32,38,39,41)(35,43,44,45)

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3373);