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Cayley diagram

D215 #88351

order430
isoclinismisoclinic class of D215
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD215
unambiguous semidirect productC5⋊D43
unambiguous semidirect productC43⋊D5

Splittings

Fitting, socle, derived, HallC5×C43 ⋊ C2
SylowC43 ⋊ D5
SylowC5 ⋊ D43

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C43C2
LCSG ▷ C5×C43
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 215

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

Polycyclic presentation:

2,5,43|b^a=b^4,c^a=c^42

Conjugacy classes & character table

109 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×D43, C2×D215, C5⋊(D43⋊C3), …
maximal normal subgroup ofD5×D43, C2×D215, C5⋊(D43⋊C3), …
maximal quotient ofDic215, C2×D215, C3×D215, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(430, 3);