C₁₃×#23794 #15710133

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#23794

Subgroups

	subgroup	G/H
center	C₈×C₁₃	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂×C₁₃	#2397
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ G

930 conjugacy classes of subgroups; only the 250 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 250 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)(14,15,18,22,19,23,31,37)(16,24,26,32,27,36,30,20)(17,21,28,34,29,35,42,45)(25,38,39,43,40,44,41,33);(14,16)(15,20)(17,25)(18,30)(19,27)(21,33)(22,36)(23,32)(24,37)(26,31)(28,41)(29,40)(34,44)(35,43)(38,45)(39,42);(20,32)(24,36)(33,43)(38,44);(14,17,18,28,19,29,31,42)(15,21,22,34,23,35,37,45)(16,25,30,41,27,40,26,39)(20,33,36,44,32,43,24,38)

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 16782);