C₁₃×#8505 #15694844

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#8505

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃	#120
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	#379
prime radical	C₁₃×#3531	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

648 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 832

A minimal faithful permutation representation — 3 generators on 61 points:

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

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1493);