C₁₃×#12889 #15699228

order	3328
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#12889

Subgroups

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

310 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 174 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) = 57
transitive degree	μ_t(G) = 3328

A minimal faithful permutation representation — 3 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27)(28,40)(29,34)(30,48)(31,51)(32,52)(33,39)(35,44)(36,41)(37,50)(38,49)(42,54)(43,53)(45,57)(46,56)(47,55);(19,22)(23,25)(26,28,41,46,32,43,50,47,33,44,31,42,49,45,30,29)(27,34,48,57,38,54,51,35,39,55,37,53,52,56,36,40);(18,20,21,24)(19,23,22,25)(26,29,30,45,49,42,31,44,33,47,50,43,32,46,41,28)(27,35,36,54,52,57,37,34,39,40,51,56,38,53,48,55)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5877);