C₁₃×#10135 #15696474

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10128
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10135

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

434 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 102 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)(30,31,36,41)(32,42,45,53)(33,38,49,56)(34,40,35,39)(37,46,52,44)(43,58,59,54)(47,61,60,51)(48,57,50,55);(14,15,18,21)(16,19,23,28)(17,25,24,20)(22,29,26,27)(30,32)(31,37)(33,47)(34,46)(35,44)(36,45)(38,54)(39,53)(40,42)(41,52)(43,48)(49,60)(50,59)(51,55)(56,58)(57,61);(14,16)(15,19)(17,26)(18,23)(20,29)(21,28)(22,24)(25,27)(30,33,36,49)(31,38,41,56)(32,43,45,59)(34,48,35,50)(37,51,52,61)(39,55,40,57)(42,54,53,58)(44,47,46,60)

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, 3123);