C₁₃×#12365 #15698704

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12364
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#12365

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1629
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₃
prime radical	C₁₃×#3291	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₈×C₁₃ ◁ G

346 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 78 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)(16,25)(17,28,30,45)(18,23)(19,33)(20,35)(21,27)(22,26,39,44)(24,32)(29,37,36,42)(31,40)(34,41,43,38);(14,16,18,27)(15,21,23,25)(17,26,30,44)(19,20,31,32)(22,37,39,42)(24,40,35,33)(28,38,45,41)(29,34,36,43);(14,17)(15,22)(16,26)(18,30)(19,34)(20,36)(21,37)(23,39)(24,41)(25,42)(27,44)(28,40)(29,32)(31,43)(33,45)(35,38)

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, 5353);