Finite Group Databasebeta

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C19×#2678 #14560535

order2432
nilpotency class2
isoclinismisoclinic class of #2668
automorphism?
homologyAbelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4

Aliases

direct productC19×#2678

Subgroups

subgroupG/H
center, socleC23×C19C24
commutator, Frattini, cosocleC23C24×C19
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C19 ◁ G

802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 608

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)(20,21,22,23)(28,29)(30,34)(31,32)(33,35);(25,27)(29,32)(30,35);(20,21)(22,23)(24,25)(26,27)(28,29)(30,33)(31,32)(34,35);(20,21)(22,23)(28,30)(29,33)(31,35)(32,34)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×#36703, C19×#36713, C19×#36714, …
maximal normal subgroup ofC19×#36703, C19×#36713, C19×#36714, …
maximal quotient ofC19×#14357, C19×#14358, C19×#14359, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1410);