Finite Group Databasebeta

← Prev (#16892090) Next (#16892092) →

C2×C17×#2382 #16892091

order4352
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28

Aliases

direct productC2×C17×#2382

Subgroups

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

2198 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);(3,4,5,6)(7,8)(9,13)(10,11)(12,14)(16,17)(20,21);(8,11)(9,14)(15,16,19,17)(18,21,22,20);(7,8)(9,12)(10,11)(13,14)(15,17,19,16)(18,21,22,20);(7,9,10,14)(8,12,11,13)(15,18,19,22)(16,20,17,21)

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 27335);