C₁₃×#12119 #15698458

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12117
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#12119

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1595
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₃
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×M₁₆ ◁ G

404 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 70 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)(17,21)(18,25)(19,24)(20,26)(22,29)(23,31)(28,40)(30,41)(32,37)(33,39)(34,36)(35,44)(38,45)(42,43);(15,21)(17,31)(18,19)(22,35)(23,25)(24,36)(26,37)(27,40)(28,43)(29,33)(32,34)(38,41)(39,42)(44,45);(14,16,20,30)(15,22,26,39)(17,28,32,45)(18,33,19,29)(21,35,37,42)(23,40,36,38)(24,41,25,27)(31,43,34,44)

Conjugacy classes & character table

325 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5107);