C₁₃×#7228 #15693567

order	3328
nilpotency class	3
isoclinism	isoclinic class of #7225
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#7228

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

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

normal subgroups only

This group has 252 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)(16,26)(17,31,33,57)(18,36)(19,24)(20,25)(21,27,39,51)(22,35,42,59)(23,44)(28,54)(29,48)(30,49)(32,46)(34,61,60,43)(37,45)(38,64)(40,67,65,75)(41,53,66,72)(47,68)(50,71)(52,74,73,63)(55,70)(56,76)(58,62,77,69);(14,16,18,28,32,50,44,68,20,30,38,56,19,29,37,55)(15,21,23,40,24,41,36,63,25,39,45,65,46,66,64,74)(17,27,34,52,59,72,69,67,33,51,60,73,35,53,62,75)(22,26,43,47,31,48,58,54,42,49,61,70,57,71,77,76)

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, 216);