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Dic221 #11725126

order884
isoclinismisoclinic class of D221
automorphismAut(G) order 84864
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic221

Splittings

derived, HallC13×C17 ⋊ C4
SylowC17 ⋊ Dic13
SylowC13 ⋊ Dic17

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D221
commutator, hypocenterC13×C17C4
Fitting, socle, prime radical, cosocleC2×C13×C17C2
LCSG ▷ C13×C17
UCSC1 ◁ C2

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 884

A minimal faithful permutation representation — 2 generators on 34 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);(1,3,2,4)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)

Polycyclic presentation:

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13183723, #13183724, D17×Dic13, …
maximal normal subgroup of#13183723, #13183724, D17×Dic13, …
maximal quotient of#13183719, C2×Dic221, C3×Dic221, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(884, 3);