C₁₃×#7107 #15693446

order	3328
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#7107

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#331
commutator	C₄²	C₂×C₈×C₁₃
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₃
prime radical	C₂×C₁₃×#127	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

294 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 416

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)(16,20,21,18)(17,19)(22,23,24,30,26,28,32,35,27,31,34,37,25,29,33,36);(14,16)(15,18)(17,21)(19,20)(23,28)(24,32)(25,26)(29,31)(30,37)(33,34)

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, 95);