C₁₃×#7263 #15693602

order	3328
nilpotency class	4
isoclinism	isoclinic class of #7262
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#7263

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#340
commutator	C₂×C₈	C₄²×C₁₃
Frattini, cosocle	C₂³×C₈	C₂²×C₁₃
prime radical	C₂⁴×C₁₃	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

336 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 106 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)(14,15)(16,18)(17,20)(19,21)(23,27,28,35)(24,31)(25,34)(29,32,30,36)(33,37);(15,18,20,19)(22,23,25,29,26,28,34,30)(24,32,31,27,33,36,37,35)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 251);