C₁₃×#7452 #15693791

order	3328
nilpotency class	5
isoclinism	isoclinic class of #7418
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₃×#7452

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃	#357
commutator	C₂×C₁₆	C₂×C₄×C₁₃
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₃
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ C₄×C₈×C₁₃ ◁ C₄×C₁₃×C₁₆ ◁ G

102 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 3328

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)(16,20)(19,21)(22,23,26,31,41,38,50,51,29,33,46,45,30,36,43,49,27,32,25,39,42,48,53,52,47,37,44,40,28,24,34,35);(14,15,17,19)(16,21,20,18)(22,24,27,36)(23,30,32,28)(25,40,26,45)(29,48,47,38)(31,44,39,46)(33,41,37,42)(34,49,43,35)(50,51,53,52)

Conjugacy classes & character table

637 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 440);