C₁₃×#13350 #15699689

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13350
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₃×#13350

Subgroups

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

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

normal subgroups only

This group has 738 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)(14,15)(16,25)(17,22)(18,21)(19,24)(20,26)(23,31)(27,38)(28,40)(29,35)(30,37)(32,45)(33,41)(34,42)(36,44)(39,43);(14,16)(15,20)(17,26)(18,27)(19,28)(21,34)(22,25)(23,32)(24,33)(29,42)(30,41)(31,43)(35,38)(36,39)(37,40)(44,45);(15,21)(18,31)(20,32)(22,35)(23,24)(25,38)(26,41)(27,43)(29,44)(33,34)(36,37)(39,40)

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, 6338);