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C17×#18162 #16875906

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

Aliases

direct productC17×#18162

Subgroups

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

1704 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 272

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

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, 11150);