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Dic187 #10625271

order748
isoclinismisoclinic class of D187
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic187
unambiguous semidirect productC11⋊Dic17

Splittings

derived, HallC11×C17 ⋊ C4
SylowC17 ⋊ Dic11
SylowC11 ⋊ Dic17

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D187
commutator, hypocenterC11×C17C4
Fitting, socle, prime radical, cosocleC2×C11×C17C2
LCSG ▷ C11×C17
UCSC1 ◁ C2

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 748

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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)

Polycyclic presentation:

2^2,11,17|a^2=b,c^a=c^10,d^a=d^16

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD17×Dic11, D11×Dic17, #13093661, …
maximal normal subgroup ofD17×Dic11, D11×Dic17, #13093661, …
maximal quotient ofC11⋊#3622, C2×Dic187, C3×Dic187, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(748, 3);