C₁₃×#7428 #15693767

order	3328
nilpotency class	5
isoclinism	isoclinic class of #7412
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#7428

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#354
commutator	C₂×C₄²	C₂×C₄×C₁₃
Frattini, cosocle	#390	C₂²×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₂×C₄² ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#390 ◁ G

226 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 46 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 — 2 generators on 37 points:

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

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 416);