Finite Group Databasebeta

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Cayley diagram

D187 #67326

order374
isoclinismisoclinic class of D187
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD187
unambiguous semidirect productC11⋊D17
unambiguous semidirect productC17⋊D11

Splittings

Fitting, socle, derived, HallC11×C17 ⋊ C2
SylowC17 ⋊ D11
SylowC11 ⋊ D17

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C17C2
LCSG ▷ C11×C17
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 187

A minimal faithful permutation representation — 2 generators on 28 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)

Polycyclic presentation:

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

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×D17, C2×D187, C3×D187, …
maximal normal subgroup ofD11×D17, C2×D187, C3×D187, …
maximal quotient ofDic187, C2×D187, C3×D187, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(374, 3);