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C19×#16293 #18022252

order4864
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C19 · Schur multiplier (H2) = C25

Aliases

direct productC19×#16293

Subgroups

subgroupG/H
center, socle, prime radicalC24×C19C24
commutator, Frattini, cosocleC24C24×C19
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C19 ◁ G

1334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 4864

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(28,29,30,31)(32,33)(34,38)(35,39)(36,37);(25,27)(28,29,30,31)(33,37)(34,39);(24,25)(26,27)(28,29)(30,31)(32,34,36,39)(33,38,37,35);(20,21)(22,23)(32,35,36,38)(33,34,37,39)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 9281);