C₁₃×#13301 #15699640

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11549
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#13301

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×Q₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

404 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 126 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)(14,15)(16,20)(17,18)(19,21)(22,23,26,29,27,30,37,33)(24,31,28,36,34,25,35,32);(15,18)(19,20)(22,24,32,23,27,34,36,30)(25,33,37,35,31,29,26,28);(14,16,17,21)(15,19,18,20)

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6289);