C₁₃×#12116 #15698455

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12114
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#12116

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

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

normal subgroups only

This group has 426 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)(16,25)(17,22)(18,30)(19,34)(20,24)(21,27)(23,32)(26,41)(28,42)(29,40)(31,36)(33,45)(35,39)(37,44)(38,43);(14,16)(15,21)(17,26)(18,31)(19,35)(20,28)(22,36)(23,39)(24,37)(25,30)(27,32)(29,44)(33,43)(34,38)(40,41)(42,45);(14,17,20,19)(15,22,24,34)(16,26,28,35)(18,32,33,29)(21,36,37,38)(23,30,40,45)(25,41,42,39)(27,43,44,31)

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, 5104);