C₁₃×#9502 #15695841

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9495
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#9502

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
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

660 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 122 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)(16,20,25,33)(17,27,29,21)(18,22)(19,23)(24,32,38,44)(26,34,37,43)(28,31)(30,35,42,36)(39,41,40,45);(14,16,19,26)(15,20,31,43)(17,24,29,39)(18,25,28,37)(21,32,35,44)(22,33,23,34)(27,41,36,45)(30,40,42,38);(14,17,28,42)(15,21,31,35)(16,24,37,38)(18,30,19,29)(20,32,43,44)(22,36,23,27)(25,40,26,39)(33,45,34,41)

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 2490);