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D627 #11929425

order1254
isoclinismisoclinic class of D627
automorphismAut(G) order 225720
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD627
unambiguous semidirect productC3⋊D209
unambiguous semidirect productC11⋊D57
unambiguous semidirect productC19⋊D33

Splittings

Fitting, socle, derived, HallC3×C11×C19 ⋊ C2
HallC11×C19 ⋊ D3
HallC3×C19 ⋊ D11
HallC3×C11 ⋊ D19
SylowC19 ⋊ D33
SylowC11 ⋊ D57
SylowC3 ⋊ D209

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C19C2
LCSG ▷ C3×C11×C19
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 627

A minimal faithful permutation representation — 2 generators on 33 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);(2,3)(5,14)(6,13)(7,12)(8,11)(9,10)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)

Polycyclic presentation:

2,3,11,19|b^a=b^2,c^a=c^10,d^a=d^18

Conjugacy classes & character table

315 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19×D33, D11×D57, D3×D209, …
maximal normal subgroup ofD19×D33, D11×D57, D3×D209, …
maximal quotient ofDic627, C2×D627, D1881, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1254, 11);