C₁₃×#12593 #15698932

order	3328
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₁₃ · Schur multiplier (H₂) = C₄²

Aliases

direct product

C₁₃×#12593

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₃	C₄²
commutator	C₄	C₂×C₄×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂³×C₁₃	C₂×M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ G

338 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 222 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)(16,19)(17,18)(20,21)(22,23,27,33,28,35,43,50,29,34,42,49,26,32,25,31)(24,36,39,52,40,30,37,46,41,48,44,45,38,47,53,51);(15,18)(19,21)(22,24)(23,30,34,47)(25,37)(26,38)(27,44)(28,40)(29,41)(31,45,50,52)(32,36,35,48)(33,51,49,46)(39,42)(43,53);(14,16,17,20)(15,19,18,21)(22,25,26,42,29,43,28,27)(23,31,32,49,34,50,35,33)(24,37,38,39,41,53,40,44)(30,45,36,46,47,52,48,51)

Conjugacy classes & character table

1144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5581);