C₁₃×#12465 #15698804

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#12465

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1677
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₃
prime radical	C₁₃×#2213	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₈×C₁₃ ◁ G

196 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 70 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)(16,26)(17,22)(18,33)(19,32)(24,44)(25,34)(27,28)(29,31)(30,38)(35,40)(36,37)(39,45)(41,42);(14,15,22,37,19,24,18,34,20,25,33,44,32,36,17,21)(16,23,38,40,28,41,27,39,30,43,26,45,29,42,31,35);(14,16)(15,23)(17,31)(18,27)(19,28)(20,30)(21,35)(22,38)(24,41)(25,43)(26,33)(29,32)(34,39)(36,42)(37,40)(44,45)

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5453);