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Cayley diagram

C13×D19 #92459

order494
isoclinismisoclinic class of D19
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D19
unambiguous semidirect productC19⋊(C2×C13)

Splittings

Fitting, socle, HallC13×C19 ⋊ C2
derived, SylowC19 ⋊ C2×C13

Subgroups

subgroupG/H
center, hypercenterC13D19
commutator, cosocle, hypocenterC19C2×C13
FrattiniC1G
Fitting, socleC13×C19C2
LCSG ▷ C19
UCSC1 ◁ C13

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 247

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32);(14,15,17,19,21,23,25,27,29,31,32,30,28,26,24,22,20,18,16)

Conjugacy classes & character table

143 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13×D19, C2×C13×D19, C13×D19⋊C3, …
maximal normal subgroup ofD13×D19, C2×C13×D19, C13×D19⋊C3, …
maximal quotient ofC13×Dic19, C2×C13×D19, C3×C13×D19, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(494, 2);