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C2×C17×#2369 #16891887

order4352
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×C17×#2369

Subgroups

subgroupG/H
center, socle, prime radicalC24×C17C24
commutatorC22C24×C4×C17
Frattini, cosocleC23C25×C17
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C17 ◁ G

2726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 4352

A minimal faithful permutation representation — 5 generators on 39 points:

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

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 27131);