C₁₃×#10676 #15697015

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#10676

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

410 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 162 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)(14,15,17,19)(16,20,21,18)(30,31,33,37,34,38,42,35)(32,39,40,44,41,45,43,36);(14,16,17,21)(15,18,19,20)(22,23)(24,26)(25,28)(27,29)(31,35)(33,42)(36,39)(37,38)(40,43)(44,45);(23,26)(24,29)(27,28)(30,32,34,41)(31,36,38,44)(33,43,42,40)(35,39,37,45)

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, 3664);