C₁₃×#7429 #15693768

order	3328
nilpotency class	5
isoclinism	isoclinic class of #7412
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#7429

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#354
commutator	C₂×C₄²	C₂×C₄×C₁₃
Frattini, cosocle	#391	C₂²×C₁₃
prime radical	C₂³×C₁₃	#99
LCS	G ▷ C₂×C₄² ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#391 ◁ G

196 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 46 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) = 53
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 2 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18,19,20)(22,23,25,30,27,32,38,48)(24,33,34,47,36,44,50,53)(26,29,40,46,41,31,39,49)(28,42,43,35,45,37,52,51);(14,15)(16,20)(17,19)(18,21)(22,24,26,35,27,36,41,51)(23,28,31,44,32,45,29,33)(25,37,39,34,38,42,40,50)(30,47,46,52,48,53,49,43)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 417);