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Cayley diagram

C5×D49 #92435

order490
isoclinismisoclinic class of D49
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D49
unambiguous semidirect productC49⋊(C2×C5)

Splittings

Fitting, HallC5×C49 ⋊ C2
derived, SylowC49 ⋊ C2×C5

Subgroups

subgroupG/H
center, hypercenterC5D49
commutator, cosocle, hypocenterC49C2×C5
FrattiniC7C5×D7
FittingC5×C49C2
socleC5×C7D7
LCSG ▷ C49
UCSC1 ◁ C5

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 54
transitive degreeμt(G) = 245

A minimal faithful permutation representation — 2 generators on 54 points:

(1,2,3,4,5)(7,9)(8,12)(10,15)(11,18)(13,21)(14,20)(16,25)(17,28)(19,30)(22,34)(23,33)(24,32)(26,37)(27,39)(29,41)(31,43)(35,44)(36,45)(38,47)(40,49)(42,51)(46,52)(48,53)(50,54);(6,11,29,50,49,28,9,8,19,42,53,39,15,14,13,31,52,47,25,24,23,22,44,45,37,26,36,35,34,33,32,16,38,46,43,21,20,10,27,48,51,30,12,7,17,40,54,41,18)

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×D49, C2×C5×D49, C5×D49⋊C3, …
maximal normal subgroup ofD5×D49, C2×C5×D49, C5×D49⋊C3, …
maximal quotient ofC5×Dic49, C2×C5×D49, C3×C5×D49, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(490, 2);