C₁₃×#7110 #15693449

order	3328
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#7110

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#327
commutator	C₂×C₈	C₂×C₈×C₁₃
Frattini, cosocle	C₂×#97	C₂²×C₁₃
prime radical	C₂²×C₁₃×D₈	C₄
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

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

normal subgroups only

This group has 270 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) = 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)(22,23,25,31,28,33,36,37,26,34,35,29,27,32,24,30);(15,18)(16,21)(19,20)(23,29)(24,35)(25,36)(27,28)(30,32)(31,34)(33,37)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 98);