Finite Group Databasebeta

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C19×#18254 #18024213

order4864
nilpotency class3
isoclinismisoclinic class of #18252
automorphism?
homologyAbelianization (H1) = C24×C19 · Schur multiplier (H2) = C26

Aliases

direct productC19×#18254

Subgroups

subgroupG/H
center, socleC22×C19C2×#120
commutator, Frattini, cosocleC22×C4C24×C19
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G

1508 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 608

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

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 11242);