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C17×#18164 #16875908

order4352
nilpotency class3
isoclinismisoclinic class of #18162
automorphism?
homologyAbelianization (H1) = C24×C17 · Schur multiplier (H2) = C26

Aliases

direct productC17×#18164

Subgroups

subgroupG/H
center, socleC22×C17C2×#120
commutator, Frattini, cosocleC22×C4C24×C17
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G

1386 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 544

A minimal faithful permutation representation — 4 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(20,21)(24,25)(30,33);(18,19)(20,23)(21,25)(22,24)(26,27)(28,30)(29,31)(32,33);(18,20,22,21)(19,23,24,25)(26,28)(27,30)(29,32)(31,33);(19,24)(23,25)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 11152);