C₁₃×#13077 #15699416

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13077
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13077

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₁₃×#3060	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

470 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 146 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)(16,26,29,41)(17,22,32,40)(18,33)(19,25)(20,38)(21,28,39,34)(23,27)(24,37)(30,31,44,35)(36,45)(42,43);(14,16,27,40,37,44,18,34,19,29,43,22,20,30,36,28)(15,21,33,31,38,17,23,41,25,39,45,35,24,32,42,26);(14,17)(15,22)(16,23)(18,35)(19,32)(20,21)(24,34)(25,40)(26,43)(27,41)(28,38)(29,42)(30,33)(31,36)(37,39)(44,45)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6065);