C₁₃×#11865 #15698204

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11858
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#11865

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

300 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 1664

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

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

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, 4853);