C₁₃×#32804 #15719143

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

Aliases

direct product

C₁₃×#32804

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

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

normal subgroups only

This group has 768 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)(32,35)(33,37)(34,36)(38,42)(39,43)(40,44)(41,45);(15,18)(16,20)(22,24)(23,26)(25,28)(27,29)(32,38)(33,40)(35,42)(37,44)(39,41)(43,45);(16,20)(19,21)(23,27)(26,29)(30,32,34,39)(31,35,36,43)(33,41,40,38)(37,45,44,42);(14,16,17,20)(15,19,18,21)(24,28)(26,29)(31,36)(35,43)(37,44)(42,45)

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, 25792);