C₁₃×#32705 #15719044

order	3328
nilpotency class	3
isoclinism	isoclinic class of #31077
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#32705

Subgroups

	subgroup	G/H
center	C₄×C₁₃	H(3,𝔽₄)
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂×C₁₃	#2804
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

536 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 194 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 — 4 generators on 45 points:

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

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 25693);