C₁₃×#7240 #15693579

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

Aliases

direct product

C₁₃×#7240

Subgroups

	subgroup	G/H
center	C₄×C₁₃	H(3,ℤ/4)
commutator	C₂×C₈	C₄²×C₁₃
Frattini, cosocle	#405	C₂²×C₁₃
socle	C₂×C₁₃	#1290
prime radical	C₂³×C₁₃	#108
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₈×C₁₃ ◁ G

148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 70 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)(14,15,18,24,20,26,41,54,21,27,42,25,35,53,19,43)(16,28,30,55,32,57,64,77,33,58,65,56,59,76,31,66)(17,34,36,67,38,50,37,52,39,68,40,70,69,23,48,49)(22,44,45,72,46,73,71,29,47,60,51,62,74,61,75,63);(14,16,19,31,35,59,42,65,21,33,41,64,20,32,18,30)(15,22,25,45,26,46,43,71,27,47,24,51,53,74,54,75)(17,29,37,61,69,72,36,60,39,63,48,73,38,62,40,44)(23,28,49,56,34,57,67,66,50,58,52,55,68,76,70,77)

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, 228);