C₁₃×#23470 #15709809

order	3328
nilpotency class	3
isoclinism	isoclinic class of #23444
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₃×#23470

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

1178 conjugacy classes of subgroups; only the 334 normal subgroups are shown.

normal subgroups only

This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 334 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 — 4 generators on 53 points:

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 16458);