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C19×#2104 #14559961

order2432
nilpotency class3
isoclinismisoclinic class of #2104
automorphism?
homologyAbelianization (H1) = C23×C19 · Schur multiplier (H2) = C2

Aliases

direct productC19×#2104

Subgroups

subgroupG/H
center, socleC2×C19#401
commutator, Frattini, cosocleC24C23×C19
prime radicalC24×C19C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C19 ◁ C24×C19 ◁ G

178 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)(22,28,30,25)(23,26,32,35)(24,27)(29,34)(31,33);(20,22)(21,25)(23,31,32,29)(24,30)(26,34,35,33)(27,28);(20,23)(21,26,27,35)(22,29)(24,32)(25,33,28,34)(30,31)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C19×#2104, C19×#23847, C19×#32700, …
maximal normal subgroup ofC2×C19×#2104, C19×#23847, C19×#32700, …
maximal quotient ofC19×#10690, C19×#10691, C19×#11318, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 836);