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Dic247 #11758342

order988
isoclinismisoclinic class of D247
automorphismAut(G) order 106704
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic247
unambiguous semidirect productC19⋊Dic13

Splittings

derived, HallC13×C19 ⋊ C4
SylowC19 ⋊ Dic13
SylowC13 ⋊ Dic19

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D247
commutator, hypocenterC13×C19C4
Fitting, socle, prime radical, cosocleC2×C13×C19C2
LCSG ▷ C13×C19
UCSC1 ◁ C2

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 988

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

Polycyclic presentation:

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

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19×Dic13, D13×Dic19, #14520340, …
maximal normal subgroup ofD19×Dic13, D13×Dic19, #14520340, …
maximal quotient ofC19⋊#1055, C2×Dic247, C3×Dic247, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(988, 3);