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C19×#1933 #14559790

order2432
nilpotency class3
isoclinismisoclinic class of #465
automorphism?
homologyAbelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C4

Aliases

direct productC19×#1933

Subgroups

subgroupG/H
center, socle, prime radicalC23×C19C2×D4
commutatorC2×C4C22×C4×C19
Frattini, cosocleC22×C4C23×C19
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G

256 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 2432

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C19×#1933, C19×#21083, C19×#21087, …
maximal normal subgroup ofC2×C19×#1933, C19×#21083, C19×#21087, …
maximal quotient ofC19×#9553, C19×#9557, C19×#9561, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 665);