C₁₃×#10523 #15696862

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10518
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#10523

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

382 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 114 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)(14,15,19,23)(16,24,21,17)(18,25,28,22)(20,27,29,26)(30,31)(32,40)(33,38)(34,37)(35,39)(36,42)(41,45)(43,44);(14,16,19,21)(15,20,23,29)(17,25,24,22)(18,27,28,26)(30,32)(31,36)(33,42)(34,43)(35,41)(37,45)(38,40)(39,44);(14,17,18,20,19,24,28,29)(15,21,22,27,23,16,25,26)(31,37)(32,41)(34,35)(38,39)(42,43)(44,45)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3511);