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D437 #11724804

order874
isoclinismisoclinic class of D437
automorphismAut(G) order 173052
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD437
unambiguous semidirect productC19⋊D23
unambiguous semidirect productC23⋊D19

Splittings

Fitting, socle, derived, HallC19×C23 ⋊ C2
SylowC23 ⋊ D19
SylowC19 ⋊ D23

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC19×C23C2
LCSG ▷ C19×C23
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 437

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42);(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)

Polycyclic presentation:

2,19,23|b^a=b^18,c^a=c^22

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19×D23, C2×D437, C3×D437, …
maximal normal subgroup ofD19×D23, C2×D437, C3×D437, …
maximal quotient ofDic437, C2×D437, C3×D437, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(874, 3);