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Cayley diagram

D247 #92460

order494
isoclinismisoclinic class of D247
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD247
unambiguous semidirect productC13⋊D19
unambiguous semidirect productC19⋊D13

Splittings

Fitting, socle, derived, HallC13×C19 ⋊ C2
SylowC19 ⋊ D13
SylowC13 ⋊ D19

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C19C2
LCSG ▷ C13×C19
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 247

A minimal faithful permutation representation — 2 generators on 32 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)

Polycyclic presentation:

2,13,19|b^a=b^12,c^a=c^18

Conjugacy classes & character table

125 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13×D19, C2×D247, (C19⋊C3)⋊D13, …
maximal normal subgroup ofD13×D19, C2×D247, (C19⋊C3)⋊D13, …
maximal quotient ofDic247, C2×D247, C3×D247, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(494, 3);