C₁₃×#13372 #15699711

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13371
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13372

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#476
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

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

normal subgroups only

This group has 370 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) = 49
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 49 points:

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

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, 6360);