C₁₃×#32805 #15719144

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₁₃×#32805

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

734 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 206 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) = 1664

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)(16,19)(17,18)(20,21)(22,23,25,27)(24,26,28,29)(30,31,34,32)(33,38,41,36)(35,37,43,39)(40,44,45,42);(15,18)(16,20)(22,24)(23,26)(25,28)(27,29)(30,32,34,31)(33,40,41,45)(35,37,43,39)(36,42,38,44);(16,20)(19,21)(23,27)(26,29)(30,33,34,41)(31,36,32,38)(35,44,43,42)(37,40,39,45);(14,16,17,20)(15,19,18,21)(24,28)(26,29)(31,32)(36,38)(37,39)(40,45)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 25793);