C₁₃×#13354 #15699693

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13353
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13354

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2021
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₃
prime radical	C₁₃×#3021	C₂
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

692 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 94 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)(15,20)(16,24)(17,27)(18,31)(21,35)(22,38)(23,28)(25,42)(26,32)(29,41)(33,36)(34,40)(37,45)(39,43);(14,15)(16,21)(17,28)(18,22)(19,23)(20,27)(24,36)(25,43)(26,37)(29,33)(30,38)(31,40)(32,39)(34,44)(35,42)(41,45);(14,16,19,26)(15,21,23,37)(17,29,27,25)(18,32,31,24)(20,33,28,43)(22,39,40,36)(30,41,44,42)(34,45,38,35)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6342);