C₁₃×#13658 #15699997

order	3328
nilpotency class	5
isoclinism	isoclinic class of #13657
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13658

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2177
commutator	C₁₆	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
prime radical	C₁₃×#2263	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₈×C₁₃ ◁ C₁₃×#346 ◁ G

194 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 45
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 45 points:

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

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, 6646);