C₁₃×#10009 #15696348

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10004
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10009

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

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

normal subgroups only

This group has 528 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)(14,15,20,25)(16,26,17,28)(18,24,19,23)(21,29,22,27)(30,31,34,38)(32,36,40,45)(33,35,41,37)(39,44,42,43);(14,16)(15,21)(17,20)(18,29)(19,27)(22,25)(23,28)(24,26)(31,35)(33,41)(36,44)(37,38)(39,42)(43,45);(14,17,20,16)(15,22,25,21)(18,29,19,27)(23,28,24,26)(30,32,34,40)(31,36,38,45)(33,42,41,39)(35,43,37,44)

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, 2997);