C₁₃×#32816 #15719155

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₄³

Aliases

direct product

C₁₃×#32816

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

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

normal subgroups only

This group has 662 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) = 61
transitive degree	μ_t(G) = 3328

A minimal faithful permutation representation — 4 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,18)(16,19,20,21)(22,23,25,27)(24,26,28,29)(30,31)(32,36)(33,43)(34,38)(35,39)(37,45)(40,58)(41,51)(42,52)(44,61)(46,57)(47,55)(48,56)(49,54)(50,59)(53,60);(15,18)(16,20)(22,24)(23,26)(25,28)(27,29)(30,32,34,41)(31,36,38,51)(33,44,45,60)(35,48,47,42)(37,53,43,61)(39,56,55,52)(40,49,59,46)(50,57,58,54);(16,20)(19,21)(23,27)(26,29)(30,33,34,45)(31,37,38,43)(32,40,41,59)(35,49,47,46)(36,50,51,58)(39,57,55,54)(42,60,48,44)(52,61,56,53);(14,16,17,20)(15,19,18,21)(24,28)(26,29)(31,38)(32,41)(37,43)(39,55)(40,59)(42,48)(44,60)(54,57)

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, 25804);