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C17×#13451 #16871195

order4352
nilpotency class4
isoclinismisoclinic class of #13304
automorphism?
homologyAbelianization (H1) = C23×C17 · Schur multiplier (H2) = C23

Aliases

direct productC17×#13451

Subgroups

subgroupG/H
center, socle, prime radicalC23×C17C2×D8
commutator, Frattini, cosocleC22×C8C23×C17
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G

382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 45 points:

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

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, 6439);