C₁₃×#12104 #15698443

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12102
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#12104

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×C₂²⋊C₈ ◁ G

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

normal subgroups only

This group has 480 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) = 37
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,21)(23,28)(24,27)(25,32)(29,37)(30,36)(31,34)(33,35);(14,15)(16,18)(17,19)(20,21)(22,23)(24,29)(25,33)(26,30)(27,35)(28,32)(31,36)(34,37);(14,16)(15,18)(17,20)(19,21)(22,24,26,27)(23,29,30,35)(25,31,34,32)(28,33,36,37)

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, 5092);