C₁₃×#33827 #15720166

order	3328
nilpotency class	4
isoclinism	isoclinic class of #33764
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#33827

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂³×C₁₃	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#117 ◁ C₁₃×#405 ◁ G

464 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 194 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) = 85
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 4 generators on 85 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,20)(22,23,28,33)(24,29,35,50)(25,38,41,72)(26,42,46,71)(27,47,44,32)(30,53,55,39)(31,56,58,45)(34,60,61,83)(36,66,64,82)(37,69,65,52)(40,73,48,57)(43,59,74,54)(49,75,76,62)(51,79,78,68)(63,84,70,80)(67,81,85,77);(14,15)(16,19)(17,18)(20,21)(22,24,28,35)(23,29,33,50)(25,34,41,61)(26,36,46,64)(27,37,44,65)(30,49,55,76)(31,51,58,78)(32,52,47,69)(38,60,72,83)(39,62,53,75)(40,63,48,70)(42,66,71,82)(43,67,74,85)(45,68,56,79)(54,77,59,81)(57,80,73,84);(15,18)(19,21)(22,25,28,41)(23,30,33,55)(24,34,35,61)(26,43,46,74)(27,48,44,40)(29,49,50,76)(31,57,58,73)(32,59,47,54)(36,67,64,85)(37,70,65,63)(38,71,72,42)(39,56,53,45)(51,80,78,84)(52,81,69,77)(60,82,83,66)(62,79,75,68);(14,16,17,20)(15,19,18,21)(24,35)(29,50)(34,61)(36,64)(37,65)(49,76)(51,78)(52,69)(60,83)(62,75)(63,70)(66,82)(67,85)(68,79)(77,81)(80,84)

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, 26815);