C₁₃×#13362 #15699701

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13360
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13362

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2021
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₃
prime radical	C₁₃×#585	C₂²
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

670 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 77
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 77 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,21,26)(16,27,31,53)(17,32,37,57)(18,38,42,24)(19,43,20,25)(22,39,49,29)(23,36,52,35)(28,60,62,76)(30,65,44,59)(33,58,66,77)(34,69,40,67)(41,55,45,56)(46,70,75,68)(47,63,48,64)(50,61,74,73)(51,71,54,72);(14,16)(15,22)(17,33)(18,39)(19,30)(20,44)(21,31)(23,50)(24,53)(25,47)(26,49)(27,38)(28,36)(29,42)(32,46)(34,70)(35,62)(37,66)(40,68)(41,64)(43,48)(45,63)(51,60)(52,74)(54,76)(55,65)(56,59)(57,75)(58,69)(61,71)(67,77)(72,73);(14,17,21,37)(15,23,26,52)(16,28,31,62)(18,40,42,34)(19,36,20,35)(22,46,49,75)(24,54,38,51)(25,57,43,32)(27,58,53,77)(29,61,39,73)(30,66,44,33)(41,71,45,72)(47,50,48,74)(55,67,56,69)(59,76,65,60)(63,70,64,68)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6350);