C₁₃×#12367 #15698706

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12366
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#12367

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1629
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₃
prime radical	C₁₃×#3293	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₈×C₁₃ ◁ G

336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 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)(16,24,26,43)(17,28)(18,31)(20,35,37,45)(21,39)(22,34)(25,30,27,42)(29,41)(32,33)(36,40,38,44);(14,15,19,23)(16,20,26,37)(17,29,33,39)(18,34,31,22)(21,28,41,32)(24,40,43,44)(25,38,27,36)(30,35,42,45);(14,16)(15,20)(17,30)(18,25)(19,26)(21,40)(22,36)(23,37)(24,32)(27,31)(28,43)(29,35)(33,42)(34,38)(39,45)(41,44)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5355);