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C19×#2356 #14560213

order2432
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23×C4

Aliases

direct productC19×#2356

Subgroups

subgroupG/H
center, socle, prime radicalC23×C19C24
commutatorC22C23×C4×C19
Frattini, cosocleC23C24×C19
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C19 ◁ G

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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)(20,21,22,23)(24,25,28,27)(26,29,31,30)(34,38)(36,39);(25,27)(29,30)(32,33,35,37)(34,36,38,39);(24,26,28,31)(25,29,27,30)(32,34,35,38)(33,36,37,39);(24,27,28,25)(26,30,31,29)

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×#8768, C19×#8769, C19×#8774, …
maximal normal subgroup ofC19×#8768, C19×#8769, C19×#8774, …
maximal quotient ofC19×#13804, C19×#13806, C19×#13810, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1088);