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C19×#2343 #14560200

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

Aliases

direct productC19×#2343

Subgroups

subgroupG/H
center, socleC23×C19C24
commutatorC22C23×C4×C19
Frattini, cosocleC23C24×C19
prime radicalC24×C19C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C19 ◁ G

532 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 1216

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

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×#17604, C19×#17609, C2×C19×#2343, …
maximal normal subgroup ofC19×#17604, C19×#17609, C2×C19×#2343, …
maximal quotient ofC19×#13799, C19×#13805, C19×#13806, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1075);