C₁₃×#12175 #15698514

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12173
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#12175

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1598
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₃
prime radical	C₁₃×#2190	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×M₁₆ ◁ G

346 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 70 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)(16,26)(17,30)(18,22)(19,24)(20,25)(21,27)(23,33)(28,42)(29,43)(31,36)(32,41)(34,40)(35,39)(37,45)(38,44);(14,16)(15,21)(17,31)(18,28)(19,35)(20,29)(22,36)(23,39)(24,37)(25,38)(26,30)(27,33)(32,45)(34,44)(40,42)(41,43);(15,22,25,24)(17,32)(21,36,38,37)(23,30,40,41)(26,42,43,39)(27,44)(31,45)(33,34)

Conjugacy classes & character table

325 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5163);