Finite Group Databasebeta

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Cayley diagram

D221 #89214

order442
isoclinismisoclinic class of D221
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD221
unambiguous semidirect productC13⋊D17
unambiguous semidirect productC17⋊D13

Splittings

Fitting, socle, derived, HallC13×C17 ⋊ C2
SylowC17 ⋊ D13
SylowC13 ⋊ D17

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C17C2
LCSG ▷ C13×C17
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 221

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

Polycyclic presentation:

2,13,17|b^a=b^12,c^a=c^16

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11725130, #11725131, D13×D17, …
maximal normal subgroup of#11725130, #11725131, D13×D17, …
maximal quotient ofDic221, C2×D221, C3×D221, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(442, 3);