C₁₃×#23795 #15710134

order	3328
nilpotency class	3
isoclinism	isoclinic class of #23414
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#23795

Subgroups

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

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

normal subgroups only

This group has 908 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)(17,21,29,35,28,34,41,44)(25,38,40,43,39,45,42,33);(14,16)(15,20)(17,25)(18,30)(19,27)(21,33)(22,36)(23,32)(24,37)(26,31)(28,39)(29,42)(34,43)(35,45)(38,44)(40,41);(17,28)(20,32)(21,34)(24,36)(25,39)(29,41)(35,44)(40,42);(14,17,18,29,19,28,31,41)(15,21,22,35,23,34,37,44)(16,25,30,42,27,39,26,40)(20,33,36,45,32,43,24,38)

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, 16783);