C₁₃×#10533 #15696872

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10530
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#10533

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

364 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 98 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 — 3 generators on 45 points:

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

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, 3521);