C₁₃×#10123 #15696462

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10123

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

442 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 61
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(16,22)(17,24)(19,27)(20,25)(23,26)(28,29)(30,31)(32,41)(33,46)(34,51)(35,39)(36,40)(37,43)(38,49)(42,59)(44,54)(45,53)(47,58)(48,57)(50,56)(52,60)(55,61);(14,15,18,21)(16,19,23,28)(17,25,24,20)(22,29,26,27)(30,32)(31,37)(33,47)(34,44)(35,43)(36,45)(38,55)(39,53)(40,54)(41,51)(42,48)(46,52)(49,60)(50,61)(56,59)(57,58);(14,16)(15,19)(17,26)(18,23)(20,29)(21,28)(22,24)(25,27)(30,33,36,50)(31,38,40,57)(32,42,45,60)(34,48,35,49)(37,52,54,59)(39,56,51,46)(41,58,53,55)(43,47,44,61)

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, 3111);