C₁₃×#12109 #15698448

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12108
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#12109

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₁₃×#2018	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₁₃×#408 ◁ G

410 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 74 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)(18,21)(23,29)(24,33)(25,36)(26,27)(30,44)(31,48)(32,43)(34,50)(35,40)(37,41)(38,39)(42,45)(46,53)(47,51);(14,15)(16,18)(17,19)(20,21)(22,23,28,32)(24,30,35,47)(25,37,39,48)(26,31,27,41)(29,38,43,36)(33,45,40,46)(34,51,50,44)(42,52,53,49);(14,16)(15,18)(17,20)(19,21)(22,24)(23,30)(25,34)(26,40)(27,33)(28,35)(29,42)(31,46)(32,47)(36,49)(37,51)(38,52)(39,50)(41,45)(43,53)(44,48)

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5097);