C₁₃×#9389 #15695728

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9385
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#9389

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#392	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

496 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 118 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)(14,15,19,24,20,22,39,40)(16,26,23,41,28,17,31,27)(18,34,36,43,21,25,38,29)(30,33,37,44,35,32,42,45);(14,16,27,34,21,30,45,22)(15,20,28,41,25,18,35,44)(17,24,36,31,32,29,39,42)(19,37,26,40,38,23,33,43);(15,22)(16,28)(17,32)(19,38)(23,42)(24,43)(25,34)(26,33)(29,40)(30,35)(31,37)(36,39)

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 2377);