C₁₃×#33982 #15720321

order	3328
nilpotency class	5
isoclinism	isoclinic class of #33982
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#33982

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	C₂²×D₁₆
commutator, Frattini, cosocle	C₁₆	C₂⁴×C₁₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₁₃×#41 ◁ C₁₃×#131 ◁ C₁₃×#504 ◁ G

472 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 202 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 — 4 generators on 77 points:

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

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 26970);