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D527 #11760460

order1054
isoclinismisoclinic class of D527
automorphismAut(G) order 252960
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD527
unambiguous semidirect productC17⋊D31
unambiguous semidirect productC31⋊D17

Splittings

Fitting, socle, derived, HallC17×C31 ⋊ C2
SylowC31 ⋊ D17
SylowC17 ⋊ D31

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC17×C31C2
LCSG ▷ C17×C31
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 527

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(19,48)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)

Polycyclic presentation:

2,17,31|b^a=b^16,c^a=c^30

Conjugacy classes & character table

265 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD17×D31, C2×D527, C3×D527, …
maximal normal subgroup ofD17×D31, C2×D527, C3×D527, …
maximal quotient ofDic527, C2×D527, C3×D527, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1054, 3);