C₁₃×#10119 #15696458

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10104
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10119

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

454 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 106 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)(16,23)(17,19)(18,28)(20,22)(21,24)(25,29)(26,27)(30,31,35,32)(33,40,41,45)(34,39,44,37)(36,43,38,42);(14,16,19,25)(15,21,17,27)(18,26,20,24)(22,29,28,23)(30,32,35,31)(33,38,41,36)(34,37,44,39)(40,43,45,42);(14,17,19,15)(16,23,25,29)(18,28,20,22)(21,24,27,26)(30,33)(31,36)(32,38)(34,43)(35,41)(37,45)(39,40)(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, 3107);