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C19×#13316 #18019275

order4864
nilpotency class4
isoclinismisoclinic class of #13316
automorphism?
homologyAbelianization (H1) = C23×C19 · Schur multiplier (H2) = C24

Aliases

direct productC19×#13316

Subgroups

subgroupG/H
center, socleC22×C19#447
commutator, Frattini, cosocleC22×C8C23×C19
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C22×M16×C19 ◁ G

604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 608

A minimal faithful permutation representation — 3 generators on 39 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)(26,29)(27,36)(28,31)(30,33)(32,35)(34,37)(38,39);(25,29)(26,33)(27,35)(30,32)(31,37)(34,39)(36,38);(21,23)(26,34)(29,37)(30,38)(33,39)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6304);