C₁₃×#12451 #15698790

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12430
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#12451

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₃
prime radical	C₂×D₄×C₁₃	D₈
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ C₈×D₄×C₁₃ ◁ G

224 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 1664

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

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

Conjugacy classes & character table

637 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5439);