C₁₃×#9517 #15695856

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9495
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9517

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₂⁴	C₂²×C₄×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

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

normal subgroups only

This group has 520 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) = 832

A minimal faithful permutation representation — 3 generators on 45 points:

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

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, 2505);