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D287 #10588115

order574
isoclinismisoclinic class of D287
automorphismAut(G) order 68880
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD287
unambiguous semidirect productC7⋊D41
unambiguous semidirect productC41⋊D7

Splittings

Fitting, socle, derived, HallC7×C41 ⋊ C2
SylowC41 ⋊ D7
SylowC7 ⋊ D41

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C41C2
LCSG ▷ C7×C41
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 287

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48);(2,7)(3,6)(4,5)(9,48)(10,47)(11,46)(12,45)(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)

Polycyclic presentation:

2,7,41|b^a=b^6,c^a=c^40

Conjugacy classes & character table

145 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×D41, C2×D287, ΓL(1,𝔽8)⋊D41, …
maximal normal subgroup ofD7×D41, C2×D287, ΓL(1,𝔽8)⋊D41, …
maximal quotient ofDic287, C2×D287, C3×D287, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(574, 3);