C₁₃×#10097 #15696436

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10088
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10097

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

542 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 102 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 — 3 generators on 45 points:

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

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3085);