C₁₃×#9196 #15695535

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9183
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#9196

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂⁴×C₁₃	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

478 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 134 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 — 3 generators on 53 points:

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

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, 2184);