C₁₃×#23840 #15710179

order	3328
nilpotency class	3
isoclinism	isoclinic class of #23391
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#23840

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

662 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 270 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 — 4 generators on 45 points:

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

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, 16828);