C₁₃×#13340 #15699679

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13340
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13340

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#493
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#2011
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

552 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 416

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

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, 6328);