C₁₃×#7812 #15694151

order	3328
nilpotency class	3
isoclinism	isoclinic class of #7734
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₃×#7812

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

398 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 106 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)(15,18)(16,20)(19,21)(23,26)(24,28)(27,29)(30,31,34,37)(32,35,39,42)(33,36,40,43)(38,44,45,41);(14,15,17,19)(16,21,20,18)(30,32)(31,35)(33,38)(34,39)(36,41)(37,42)(40,45)(43,44);(22,23,25,27)(24,29,28,26)(30,33)(31,36)(32,38)(34,40)(35,41)(37,43)(39,45)(42,44)

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, 800);