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D323 #10619479

order646
isoclinismisoclinic class of D323
automorphismAut(G) order 93024
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD323
unambiguous semidirect productC17⋊D19
unambiguous semidirect productC19⋊D17

Splittings

Fitting, socle, derived, HallC17×C19 ⋊ C2
SylowC19 ⋊ D17
SylowC17 ⋊ D19

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC17×C19C2
LCSG ▷ C17×C19
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 323

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);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)

Polycyclic presentation:

2,17,19|b^a=b^16,c^a=c^18

Conjugacy classes & character table

163 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD17×D19, C2×D323, C17⋊(D19⋊C3), …
maximal normal subgroup ofD17×D19, C2×D323, C17⋊(D19⋊C3), …
maximal quotient ofDic323, C2×D323, C3×D323, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(646, 3);