C₁₃×#13366 #15699705

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

Aliases

direct product

C₁₃×#13366

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

382 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 130 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)(18,19,21,23)(20,24,25,22)(26,27,29,32)(28,36,37,54)(30,42,40,55)(31,45,41,35)(33,49,47,38)(34,51,48,44)(39,56,46,52)(43,53,57,50);(14,15)(16,17)(18,20,21,25)(19,22,23,24)(27,32)(33,47)(34,48)(35,45)(36,54)(42,55)(50,53)(52,56);(15,17)(26,28,29,37)(27,33,32,47)(30,43,40,57)(31,46,41,39)(34,52,48,56)(35,53,45,50)(36,55,54,42)(38,51,49,44)

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, 6354);