C₁₃×#32869 #15719208

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

Aliases

direct product

C₁₃×#32869

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 ◁ C₁₃×#376 ◁ G

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

normal subgroups only

This group has 562 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) = 3328

A minimal faithful permutation representation — 4 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,20)(16,19,21,18)(22,23)(24,27)(25,26)(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)(23,26)(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)(23,26)(24,28)(30,33,36,31)(32,39,41,45)(34,43,35,38)(37,44,42,40);(16,21)(18,19)(22,24,25,28)(23,27,26,29)(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, 25857);