C₁₃×#32814 #15719153

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₄³

Aliases

direct product

C₁₃×#32814

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

830 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 206 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) = 1664

A minimal faithful permutation representation — 4 generators on 45 points:

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

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, 25802);