C₁₃×#8529 #15694868

order	3328
nilpotency class	3
isoclinism	isoclinic class of #8528
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#8529

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#379
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#3553	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

648 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 832

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

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

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1517);