C₁₃×#32717 #15719056

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

Aliases

direct product

C₁₃×#32717

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₁₃×#41 ◁ G

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

normal subgroups only

This group has 848 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)(17,20)(18,21)(22,23)(24,26)(25,27)(28,29)(30,31,36,33)(32,37,41,42)(34,43,35,38)(39,44,45,40);(14,16)(15,18)(17,21)(19,20)(22,24)(23,26)(25,28)(27,29)(30,32,36,41)(31,37,33,42)(34,40,35,44)(38,45,43,39);(14,16)(15,19)(17,21)(18,20)(23,27)(26,29)(30,33,36,31)(32,39,41,45)(34,43,35,38)(37,44,42,40);(16,21)(18,19)(24,28)(26,29)(30,34,36,35)(31,38,33,43)(32,40,41,44)(37,45,42,39)

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, 25705);