C₁₃×#8750 #15695089

order	3328
nilpotency class	3
isoclinism	isoclinic class of #8746
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#8750

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#381
commutator	C₂⁴	C₂²×C₄×C₁₃
Frattini, cosocle	C₂⁵	C₂³×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂⁵×C₁₃ ◁ G

538 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 416

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)(16,24,26,20)(17,28,30,34)(18,22)(19,23)(21,29,35,45)(25,39,41,37)(27,38,43,33)(31,36)(32,40,44,42);(14,16,19,27)(15,20,23,33)(17,25,30,42)(18,26,31,43)(21,32,35,39)(22,24,36,38)(28,44,34,37)(29,40,45,41);(14,17)(15,21,22,34)(16,25)(18,29)(19,30)(20,32,24,37)(23,35,36,28)(26,40)(27,42)(31,45)(33,39,38,44)(41,43)

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, 1738);