C₁₃×#13654 #15699993

order	3328
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13654

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×D₁₆
commutator	C₁₆	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
prime radical	C₂×C₁₃×D₃₂	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ C₄×C₈×C₁₃ ◁ C₄×C₁₃×C₁₆ ◁ G

212 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 49
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19,21,25)(20,24,31,37)(22,35,33,49)(23,36,34,28)(26,42,40,29)(27,44,41,30)(32,45,46,39)(38,48,43,47);(19,24)(20,29)(22,30)(23,34)(25,37)(26,27)(28,45)(31,42)(32,48)(33,44)(35,38)(36,39)(40,41)(43,49)(46,47);(14,16,17,15)(19,25)(24,37)(26,40)(27,41)(28,36)(35,49)(38,43)(39,45)

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6642);