C₁₃×#9514 #15695853

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×#9514

Subgroups

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

478 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 118 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)(16,19,23,26)(17,20)(18,21)(22,25,28,29)(24,27)(30,31,34,38,35,32,36,40)(33,39,42,45,41,37,43,44);(14,16,18,23)(15,19)(17,22,24,28)(20,25)(21,26)(27,29)(30,32,34,40,35,31,36,38)(33,39,43,44,41,37,42,45);(14,17,18,24)(15,20,21,27)(16,22,23,28)(19,25,26,29)(30,33)(31,37)(32,39)(34,43)(35,41)(36,42)(38,45)(40,44)

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, 2502);