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C25×D13⋊C3 #14519591

order1950
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×D13⋊C3
unambiguous semidirect productD13⋊(C3×C25)
unambiguous semidirect product(C13⋊C3)⋊(C2×C25)
unambiguous semidirect product(C25×D13)⋊C3

Splittings

Fitting, HallC13×C25 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C25
HallC25×C13⋊C3 ⋊ C2
HallC25×D13 ⋊ C3
HallC13⋊C3 ⋊ C2×C25
HallD13 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC25D13⋊C3
commutator, hypocenterC13C2×C3×C25
FrattiniC5C5×D13⋊C3
FittingC13×C25C2×C3
socle, cosocleC5×C13C2×C3×C5
prime radicalC5×D13⋊C3C5
LCSG ▷ C13
UCSC1 ◁ C25

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:

(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)(27,31,32,28,29,33)(30,37,36,34,35,38);(26,27,30,29,33,36,35,37,38,32,31,34,28)

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC25×AGL(1,𝔽13), #13049904⋊C3, D25×D13⋊C3, …
maximal normal subgroup ofC25×AGL(1,𝔽13), #13049904⋊C3, D25×D13⋊C3, …
maximal quotient ofC25×Dic13⋊C3, C2×C25×D13⋊C3, C7×C25×D13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1950, 1);