Finite Group Databasebeta

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C19×#3542 #14561399

order2432
nilpotency class2
isoclinismisoclinic class of #3532
automorphism?
homologyAbelianization (H1) = C25×C19 · Schur multiplier (H2) = C28

Aliases

direct productC19×#3542

Subgroups

subgroupG/H
center, socleC22×C19C25
commutator, Frattini, cosocleC22C25×C19
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ G

1160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 generators on 35 points:

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×#61609, C19×#61611, C19×#61614, …
maximal normal subgroup ofC19×#61609, C19×#61611, C19×#61614, …
maximal quotient ofC19×#34362, C19×#34363, C19×#34404, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2274);