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C19×#18626 #18024585

order4864
nilpotency class3
isoclinismisoclinic class of #18618
automorphism?
homologyAbelianization (H1) = C24×C19 · Schur multiplier (H2) = C25

Aliases

direct productC19×#18626

Subgroups

subgroupG/H
center, socleC22×C19C2×#120
commutator, Frattini, cosocleC42C24×C19
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G

1088 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)(21,25)(22,23)(26,27)(29,32)(30,34)(33,35);(20,21,24,27)(22,25,23,26)(30,34)(32,35);(20,22,24,23)(21,25,27,26)(28,29)(30,35)(31,33)(32,34);(20,22,24,23)(21,26,27,25)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 11614);