C₁₃×#7229 #15693568

order	3328
nilpotency class	3
isoclinism	isoclinic class of #7225
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#7229

Subgroups

	subgroup	G/H
center	C₄×C₁₃	H(3,ℤ/4)
commutator	C₂×C₈	C₄²×C₁₃
Frattini, cosocle	C₂×#131	C₂²×C₁₃
socle	C₂×C₁₃	#1289
prime radical	C₂×C₁₃×#41	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₈×C₁₃ ◁ G

244 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 77
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 2 generators on 77 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,23,20,25,32,48)(16,26,28,50,30,52,53,69)(17,31,33,22,36,45,35,47)(19,38,37,49,39,67,61,24)(21,40,41,27,44,54,43,56)(29,58,57,73,59,77,74,51)(34,63,62,60,65,46,64,72)(42,55,70,75,71,76,66,68);(14,16,19,29,32,53,61,74,20,30,39,59,18,28,37,57)(15,21,24,42,23,43,38,66,25,44,49,71,48,41,67,70)(17,27,34,55,33,54,62,75,36,56,65,76,35,40,64,68)(22,26,46,51,31,50,60,58,47,52,63,73,45,69,72,77)

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, 217);