Finite Group Databasebeta

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C19×#3068 #14560925

order2432
nilpotency class3
isoclinismisoclinic class of #3068
automorphism?
homologyAbelianization (H1) = C24×C19 · Schur multiplier (H2) = C25

Aliases

direct productC19×#3068

Subgroups

subgroupG/H
center, socleC2×C19C2×#121
commutator, Frattini, cosocleC2×C4C24×C19
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G

466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 304

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×#24420, C19×#24422, C19×#24472, …
maximal normal subgroup ofC19×#24420, C19×#24422, C19×#24472, …
maximal quotient ofC19×#19162, C19×#19165, C19×#19166, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1800);