Finite Group Databasebeta

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C3×C11×C25×D19 #44535432

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C25×D19

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C11×C25D19
commutator, hypocenterC19C2×C3×C11×C25
FrattiniC5C3×C5×C11×D19
FittingC3×C11×C19×C25C2
socleC3×C5×C11×C19C2×C5
prime radicalC3×C5×C11×D19C5
cosocleC5×C19C2×C3×C5×C11
LCSG ▷ C19
UCSC1 ◁ C3×C11×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15675

Conjugacy classes & character table

9075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 5);