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Dic299 #11924765

order1196
isoclinismisoclinic class of D299
automorphismAut(G) order 157872
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic299
unambiguous semidirect productC23⋊Dic13

Splittings

derived, HallC13×C23 ⋊ C4
SylowC23 ⋊ Dic13
SylowC13 ⋊ Dic23

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D299
commutator, hypocenterC13×C23C4
Fitting, socle, prime radical, cosocleC2×C13×C23C2
LCSG ▷ C13×C23
UCSC1 ◁ C2

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 1196

A minimal faithful permutation representation — 2 generators on 40 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);(1,3,2,4)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)

Polycyclic presentation:

2^2,13,23|a^2=b,c^a=c^12,d^a=d^22

Conjugacy classes & character table

302 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23⋊(Dic13⋊C3), C3×Dic299, Dic897, …
maximal normal subgroup ofC23⋊(Dic13⋊C3), C3×Dic299, C11×Dic299, …
maximal quotient ofC3×Dic299, Dic897, C11×Dic299, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1196, 3);