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C17×#24817 #16882561

order4352
nilpotency class3
isoclinismisoclinic class of #23848
automorphism?
homologyAbelianization (H1) = C24×C17 · Schur multiplier (H2) = C24

Aliases

direct productC17×#24817

Subgroups

subgroupG/H
center, socle, prime radicalC23×C17C22×D4
commutator, Frattini, cosocleC22×C4C24×C17
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C17 ◁ C4×C4⋊C4×C17 ◁ G

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 4352

A minimal faithful permutation representation — 4 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(22,23,26,29)(24,28,25,27);(22,24,26,25)(23,27,29,28)(30,31,34,37)(32,38,40,45)(33,41,43,36)(35,42,44,39);(19,21)(30,32,34,40)(31,35,37,44)(33,42,43,39)(36,45,41,38);(22,25,26,24)(23,28,29,27)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 17805);