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Cayley diagram

D5×C13⋊C3 #87609

order390
isoclinismisoclinic class of D5×C13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productD5×C13⋊C3
unambiguous semidirect productC5⋊(C2×C13⋊C3)
unambiguous semidirect product(D5×C13)⋊C3

Splittings

Fitting, socle, derived, HallC5×C13 ⋊ C2×C3
HallC5×C13⋊C3 ⋊ C2
HallD5×C13 ⋊ C3
SylowC13 ⋊ C3×D5
SylowC5 ⋊ C2×C13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C13C2×C3
LCSG ▷ C5×C13
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 65

A minimal faithful permutation representation — 2 generators on 18 points:

(2,3)(4,5)(7,8,10)(9,12,15)(11,14,13)(16,18,17);(1,2,4,5,3)(6,7,9,8,11,15,12,16,18,10,13,17,14)

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C13⋊C3, #63120⋊C3, D5×D13⋊C3, …
maximal normal subgroup ofAGL(1,𝔽5)×C13⋊C3, #63120⋊C3, D5×D13⋊C3, …
maximal quotient ofDic5×C13⋊C3, C2×D5×C13⋊C3, D5×C13⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(390, 2);