Finite Group Databasebeta

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D25×#10625203 #49150210

order37050
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productD25×#10625203
unambiguous semidirect productC25⋊(C2×#10625203)

Splittings

Fitting, derived, HallC13×C19×C25 ⋊ C2×C3
HallC25×#10625203 ⋊ C2
HallC13×C19×D25 ⋊ C3
HallC19×D25 ⋊ C13⋊C3
HallC13×D25 ⋊ C19⋊C3
HallC19×C25 ⋊ C2×C13⋊C3
HallC13×C25 ⋊ C2×C19⋊C3
HallC13×C19 ⋊ C3×D25
SylowC25 ⋊ C2×#10625203
SylowC19 ⋊ C13⋊C3×D25
SylowC13 ⋊ D25×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC13×C19×C25C2×C3
FrattiniC5D5×#10625203
socleC5×C13×C19C3×D5
LCSG ▷ C13×C19×C25
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6175

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 36);