Finite Group Databasebeta

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C25×D627 #44535442

order31350
automorphism?
homologyAbelianization (H1) = C2×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×D627
unambiguous semidirect productC3⋊(C25×D209)
unambiguous semidirect productC19⋊(C25×D33)

Splittings

Fitting, HallC3×C11×C19×C25 ⋊ C2
derived, HallC3×C11×C19 ⋊ C2×C25
HallC11×C19×C25 ⋊ D3
HallC3×C19×C25 ⋊ D11
HallC3×C11×C25 ⋊ D19
HallC19×C25 ⋊ D33
HallC11×C25 ⋊ D57
HallC11×C19 ⋊ D3×C25
HallC3×C25 ⋊ D209
HallC3×C19 ⋊ D11×C25
HallC3×C11 ⋊ C25×D19
SylowC19 ⋊ C25×D33
SylowC11 ⋊ C25×D57
SylowC3 ⋊ C25×D209

Subgroups

subgroupG/H
center, hypercenterC25D627
commutator, hypocenterC3×C11×C19C2×C25
FrattiniC5C5×D627
FittingC3×C11×C19×C25C2
socle, cosocleC3×C5×C11×C19C2×C5
prime radicalC5×D627C5
LCSG ▷ C3×C11×C19
UCSC1 ◁ C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15675

Conjugacy classes & character table

7875 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 15);