C₁₃×#12046 #15698385

order	3328
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#12046

Subgroups

	subgroup	G/H
center	C₁₃×C₁₆	D₈
commutator	C₈	C₂²×C₈×C₁₃
Frattini, cosocle	C₄×C₈	C₂³×C₁₃
socle	C₂×C₁₃	C₈×D₈
prime radical	C₁₃×#508	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₃×C₁₆ ◁ C₂×C₁₃×C₁₆ ◁ C₄×C₁₃×C₁₆ ◁ G

216 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 106 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)(14,15,19,25,21,26,37,24,22,27,18,36,20,16,28,30)(17,23,32,39,34,40,45,38,35,41,31,44,33,29,42,43);(14,16)(15,21)(17,29)(18,24)(19,30)(20,27)(22,26)(23,34)(25,37)(28,36)(31,38)(32,43)(33,41)(35,40)(39,45)(42,44);(14,17,19,32,21,34,37,45,22,35,18,31,20,33,28,42)(15,23,25,39,26,40,24,38,27,41,36,44,16,29,30,43)

Conjugacy classes & character table

1144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5034);