C₁₃×#11497 #15697836

order	3328
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#11497

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

288 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 130 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)(23,28,29,26)(25,27)(30,31,35,41,37,40,50,39,36,42,49,58,34,51,33,48)(32,43,46,59,45,38,53,55,47,57,61,54,52,56,44,60);(14,16,18,24)(15,19,21,22)(17,23,25,29)(20,26,27,28)(30,32,36,47)(31,38,42,56)(33,44,50,53)(34,52,37,45)(35,46,49,61)(39,54,48,59)(40,57,51,43)(41,55,58,60);(14,17,18,25)(15,20,21,27)(16,23,24,29)(19,26,22,28)(30,33,34,49,36,50,37,35)(31,39,51,41,42,48,40,58)(32,44,52,61,47,53,45,46)(38,54,43,55,56,59,57,60)

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4485);