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C13⋊C3×D25 #14519592

order1950
isoclinismisoclinic class of C13⋊C3×D25
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×D25
unambiguous semidirect productC25⋊(C2×C13⋊C3)
unambiguous semidirect product(C13×D25)⋊C3

Splittings

Fitting, derived, HallC13×C25 ⋊ C2×C3
HallC25×C13⋊C3 ⋊ C2
HallC13×D25 ⋊ C3
SylowC25 ⋊ C2×C13⋊C3
SylowC13 ⋊ C3×D25

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC13×C25C2×C3
FrattiniC5D5×C13⋊C3
socleC5×C13C3×D5
LCSG ▷ C13×C25
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 325

A minimal faithful permutation representation — 2 generators on 38 points:

(2,3,5)(4,7,10)(6,9,8)(11,13,12)(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);(1,2,4,3,6,10,7,11,13,5,8,12,9)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13⋊C3×#1035, #13049906⋊C3, D25×D13⋊C3, …
maximal normal subgroup ofC13⋊C3×#1035, #13049906⋊C3, D25×D13⋊C3, …
maximal quotient ofC13⋊C3×Dic25, C2×C13⋊C3×D25, C7×C13⋊C3×D25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1950, 2);