C₁₃×#13330 #15699669

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13330

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

558 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 146 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) = 53
transitive degree	μ_t(G) = 3328

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(22,23,28,33)(24,34,25,37)(26,40,45,53)(27,46,43,32)(29,38,30,35)(31,49,52,44)(36,51,39,50)(41,48,42,47);(15,17)(18,19)(20,21)(22,24,28,25)(23,29,33,30)(26,41,45,42)(27,39,43,36)(31,50,52,51)(32,48,46,47)(34,53,37,40)(35,49,38,44);(19,21)(22,25,28,24)(23,30,33,29)(26,42,45,41)(27,36,43,39)(31,51,52,50)(32,47,46,48)(34,40,37,53)(35,44,38,49)

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6318);