C₁₃×#11504 #15697843

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11502
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#11504

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₃
prime radical	C₂⁴×C₁₃	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

510 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 110 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)(24,32)(25,29)(26,39,40,30)(27,31)(28,34,42,49)(33,46)(35,47)(36,50)(37,52,53,44)(38,45)(41,48,43,51);(22,24,27,35)(23,28,31,42)(25,36,38,33)(26,34,40,49)(29,43,45,41)(30,32,39,47)(37,51,53,48)(44,50,52,46);(15,18)(19,21)(22,25,27,38)(23,29,31,45)(24,33,35,36)(26,37,40,53)(28,41,42,43)(30,44,39,52)(32,46,47,50)(34,48,49,51)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4492);