C₁₃×#10120 #15696459

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10120

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

578 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 832

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

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

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3108);