C₁₃×#9518 #15695857

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9495
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9518

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₂⁴	C₂²×C₄×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

518 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 832

A minimal faithful permutation representation — 3 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,23,19,22,17,21)(16,20,24,27,25,28,26,29)(30,31)(32,35,39,43)(33,40,41,36)(34,37)(38,42)(44,45);(14,16,17,24,19,25,18,26)(15,20,23,29,22,28,21,27)(30,32,34,39)(31,35)(33,38,41,44)(36,42)(37,43)(40,45);(14,17,19,18)(15,21,22,23)(16,24,25,26)(20,27,28,29)(30,33,34,41)(31,36,37,40)(32,38,39,44)(35,42,43,45)

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, 2506);