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C19×#2069 #14559926

order2432
nilpotency class3
isoclinismisoclinic class of #2069
automorphism?
homologyAbelianization (H1) = C23×C19 · Schur multiplier (H2) = C22

Aliases

direct productC19×#2069

Subgroups

subgroupG/H
center, socleC2×C19#396
commutator, Frattini, cosocleC22×C4C23×C19
prime radicalC22×D4×C19C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 304

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C19×#2069, C19×#23622, C19×#24808, …
maximal normal subgroup ofC2×C19×#2069, C19×#23622, C19×#24808, …
maximal quotient ofC19×#10603, C19×#10605, C19×#10607, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 801);