Finite Group Databasebeta

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C19×#1920 #14559777

order2432
nilpotency class3
isoclinismisoclinic class of #447
automorphism?
homologyAbelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C4

Aliases

direct productC19×#1920

Subgroups

subgroupG/H
center, socle, prime radicalC23×C19C2×D4
commutatorC2×C4C22×C4×C19
Frattini, cosocleC22×C4C23×C19
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G

230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 2432

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C19×#1920, C19×#21032, C19×#21033, …
maximal normal subgroup ofC2×C19×#1920, C19×#21032, C19×#21033, …
maximal quotient ofC19×#9535, C19×#9539, C19×#10806, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 652);