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C19×#2990 #14560847

order2432
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24

Aliases

direct productC19×#2990

Subgroups

subgroupG/H
centerC2×C4×C19C24
commutatorC22C23×C4×C19
Frattini, cosocleC2×C4C24×C19
socleC22×C19C23×C4
prime radicalC2×#41×C19C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C19 ◁ G

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 1216

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×#8898, C19×#8900, C19×#8969, …
maximal normal subgroup ofC19×#8898, C19×#8900, C19×#8969, …
maximal quotient ofC19×#20546, C19×#20550, C19×#20558, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1722);