C₁₃×#13634 #15699973

order	3328
nilpotency class	5
isoclinism	isoclinic class of #2263
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13634

Subgroups

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

194 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 126 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)(14,15,16,17)(19,24)(20,25)(21,29)(22,32)(26,34)(27,43)(28,44)(30,46)(31,40)(33,45)(35,36)(37,42)(38,39)(41,49)(47,48);(18,19,25,36,21,27,38,44,32,42,46,49,45,47,31,34,23,26,40,48,33,41,30,37,22,28,39,43,29,35,20,24);(19,26)(24,34)(27,41)(28,42)(35,47)(36,48)(37,44)(43,49)

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, 6622);