C₁₃×#19006 #15705345

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

Aliases

direct product

C₁₃×#19006

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#562	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

938 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 222 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 — 4 generators on 45 points:

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

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, 11994);