C₁₃×#12110 #15698449

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

Aliases

direct product

C₁₃×#12110

Subgroups

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

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

normal subgroups only

This group has 422 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)(22,23)(24,35)(25,29)(26,33)(27,32)(28,34)(30,37)(31,39)(36,49)(38,50)(40,47)(41,45)(42,46)(43,48)(44,53)(51,52);(14,15)(16,18)(17,19)(20,21)(23,29)(25,39)(26,27)(30,44)(31,33)(32,45)(34,46)(35,49)(36,52)(37,43)(40,53)(41,42)(47,50)(48,51);(14,16)(15,18)(17,20)(19,21)(22,24,28,38)(23,30,34,48)(25,40,42,36)(26,43,27,37)(29,44,46,51)(31,49,45,47)(32,50,33,35)(39,53,41,52)

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, 5098);