Finite Group Databasebeta

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C3×C25×D209 #44535434

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C25×D209

Splittings

Fitting, HallC3×C11×C19×C25 ⋊ C2
derived, HallC11×C19 ⋊ C2×C3×C25
HallC11×C19×C25 ⋊ C2×C3
HallC3×C19×C25 ⋊ D11
HallC3×C11×C25 ⋊ D19
HallC3×C11×C19 ⋊ C2×C25
HallC19×C25 ⋊ C3×D11
HallC11×C25 ⋊ C3×D19
HallC3×C19 ⋊ D11×C25
HallC3×C11 ⋊ C25×D19
SylowC19 ⋊ C3×D11×C25
SylowC11 ⋊ C3×C25×D19

Subgroups

subgroupG/H
center, hypercenterC3×C25D209
commutator, hypocenterC11×C19C2×C3×C25
FrattiniC5C3×C5×D209
FittingC3×C11×C19×C25C2
socleC3×C5×C11×C19C2×C5
prime radicalC3×C5×D209C5
cosocleC5×C11×C19C2×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C3×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15675

Conjugacy classes & character table

7950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 7);