C₁₃×#12482 #15698821

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12433
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#12482

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₃
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ C₈×Q₈×C₁₃ ◁ G

200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 45
transitive degree	μ_t(G) = 3328

A minimal faithful permutation representation — 3 generators on 45 points:

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

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5470);