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C17×#18554 #16876298

order4352
nilpotency class3
isoclinismisoclinic class of #18524
automorphism?
homologyAbelianization (H1) = C24×C17 · Schur multiplier (H2) = C25

Aliases

direct productC17×#18554

Subgroups

subgroupG/H
center, socleC22×C17C2×#120
commutator, Frattini, cosocleC42C24×C17
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G

1244 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 1088

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)(18,19)(20,22)(21,23)(24,25)(27,31)(28,29)(32,33);(19,22)(20,25)(23,24)(26,27)(28,31)(29,33)(30,32);(26,27)(28,31)(29,33)(30,32);(19,23)(22,24)(26,28,30,29)(27,31,32,33)

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, 11542);